Washington (CNN) Major differences between special counsel Robert Mueller and Attorney General William Barr came into focus this week as they both deal with the fallout of the Russia investigation.

Those differences took center stage with Mueller's televised speech -- his first and perhaps final public word on the investigation -- and an extensive television interview Barr gave to CBS News . They disagreed on consequential topics that played a major role in the investigation, like whether the probe should have finished with a conclusion on whether to charge President Donald Trump.

Here's a breakdown of five critical topics where Barr and Mueller aren't on the same page:

Mueller's non-decision on obstruction

Barr and Mueller had very different views of how to approach the obstruction of justice investigation. Barr rejected much of Mueller's legal analysis, which Mueller spelled out in the report and repeated again on Wednesday.

Mueller believed that there were "difficult issues" preventing him from offering a traditional recommendation on whether to charge Trump, while Barr thought Mueller could have reached a conclusion. In fact, after Mueller submitted his report, Barr offered his own conclusion on obstruction: No charges.

Barr's comments

CBS NEWS CORRESPONDENT JAN CRAWFORD: What is the fundamental difference? Why...I mean, he said he couldn't exonerate the President. That he had looked at the evil there -- these 11 instances of possible obstruction. He couldn't exonerate the President, if he could he would've stated so. You looked at that evidence and you did. I mean, what is the fundamental difference between your view and his?

BARR: Well, I think Bob said that he was not going to engage in the analysis. He was, he was not going to make a determination one way or the other. And he also said that he could not say that the President was clearly did not violate the law, which of course is not the standard we use at the department. We have to determine whether there is clear violation of the law and so we applied the standards we would normally apply. We analyzed the law and the facts and a group of us spent a lot of time doing that and determined that both as a matter of law, many of the instances would not amount to obstruction.

CRAWFORD: As a matter of law?

BARR: As a matter of law. In other words, we didn't agree with the legal analysis -- a lot of the legal analysis in the report. It did not reflect the views of the department. It was the views of a particular lawyer or lawyers and so we applied what we thought was the right law but then we didn't rely on that. We also looked at all the facts, tried to determine whether the government could establish all the elements and as to each of those episodes we felt that the evidence was deficient.

Mueller's comments

MUELLER REPORT: ...we considered whether to evaluate the conduct we investigated under the Justice Manual standards governing prosecution and declination decisions, but we determined not to apply an approach that could potentially result in a judgment that the President committed crimes. The threshold step under the Justice Manual standards is to assess whether a person's conduct "constitutes a federal offense." US Dep't of Justice, Justice Manual§ 9-27.220 (2018) (Justice Manual). Fairness concerns counseled against potentially reaching that judgment when no charges can be brought. The ordinary means for an individual to respond to an accusation is through a speedy and public trial, with all the procedural protections that surround a criminal case. An individual who believes he was wrongly accused can use that process to seek to clear his name. In contrast, a prosecutor's judgment that crimes were committed, but that no charges will be brought, affords no such adversarial opportunity for public name-clearing before an impartial adjudicator.

MUELLER PRESS CONFERENCE: Beyond department policy, we were guided by principles of fairness. It would be unfair to potentially -- it would be unfair to potentially accuse somebody of a crime when there can be no court resolution of the actual charge. So that was Justice Department policy. Those were the principles under which we operated. And from them, we concluded that we would -- would not reach a determination one way or the other about whether the President committed a crime.

Role of Justice Department guidelines

Barr has leaned heavily on the idea that Mueller did not feel Justice Department guidelines against indicting a president are what prevented him from charging Trump with obstruction. But Mueller has undercut that narrative, making clear in his comments and in his report that the guidelines had a significant influence on his decision-making.

Mueller suggested the guidelines, which have been around since the Nixon administration, tied his hands from the very start from even considering whether a crime had been committed by Trump.

Barr's comments

BARR: The so-called discrepancy was that I had, I had testified earlier that Bob had assured me that he had not reached a decision that there was a crime committed but was not willing to pursue it simply because of the (Office of Legal Counsel) opinion and that remains the fact. That's what his position is. That's consistent with what he said yesterday. And it certainly is consistent with the joint release we put out. The confusion arose because what Bob Mueller's position was was that the OLC opinion coupled with other things as a prudential matter made him feel that he shouldn't even get into the analysis of whether something was a crime or not and that's a different question than --

CRAWFORD: Right, because you...just because there's evidence of obstruction or crime was committed doesn't mean the person is going to be charged or indicted or found to have committed that crime.

BARR: Right and he didn't even get into that analysis. In other words, what I was discussing earlier was, was Bob, did Bob make a decision there was a crime and the only reason he wasn't saying that was because of the OLC opinion. The fact is Bob did not make a decision that there was a crime. He didn't get into the analysis at all. Part of the reason for that was his judgment about the OLC opinion coupled with other things he just didn't think it was proper exercise of his authority. So it's a totally different issue and that's why, that's why both us feel that this idea that there's been a discrepancy over the OLC opinion is simply wrong.

Mueller's comments

MUELLER REPORT: First, a traditional prosecution or declination decision entails a binary determination to initiate or decline a prosecution, but we determined not to make a traditional prosecutorial judgment. The Office of Legal Counsel (OLC) has issued an opinion finding that "the indictment or criminal prosecution of a sitting President would impermissibly undermine the capacity of the executive branch to perform its constitutionally assigned functions" in violation of "the constitutional separation of powers." Given the role of the Special Counsel as an attorney in the Department of Justice and the framework of the Special Counsel regulations, see 28 U.S.C. § 515; 28 C.F.R. § 600.7(a), this Office accepted OLC's legal conclusion for the purpose of exercising prosecutorial jurisdiction. And apart from OLC's constitutional view, we recognized that a federal criminal accusation against a sitting President would place burdens on the President's capacity to govern and potentially preempt constitutional processes for addressing presidential misconduct.

MUELLER PRESS CONFERENCE: We did not, however, make a determination as to whether the President did commit a crime. The introduction to the volume two of our report explains that decision. It explains that under longstanding department policy, a President cannot be charged with a federal crime while he is in office. That is unconstitutional. Even if the charge is kept under seal and hidden from public view, that, too, is prohibited. The Special Counsel's Office is part of the Department of Justice and by regulation, it was bound by that department policy. Charging the President with a crime was therefore not an option we could consider.

Presidential powers in the Constitution

Before he became attorney general, Barr wrote a letter to senior Justice Department officials explaining his belief that a president can't commit a crime by carrying out actions that he is constitutionally allowed to take. This is an expansive view of a president's powers under Article II of the Constitution, and Barr repeated it again this week.

But it wasn't shared by Mueller. In the report, Mueller said explicitly that there were limits on Article II powers and cited Supreme Court decisions and other legal precedent to justify his probe of the President.

Barr's comments

BARR: Well let's take the firing of former FBI Director James Comey for example I think we would have said as a matter of law, and I'm not relying on my - my legal memo that I wrote as a private citizen but really on the views within the department of the people who think about these things and are responsible for framing the views of the department, and I think we would have said that as a matter of law the obstruction statutes do not reach facially valid exercise of core presidential authority or official authority even, decisions by the attorney general in administering the executive branch or litigation. But we didn't rely on that, we then looked at that issue.

Mueller's comments

MUELLER REPORT: First, the investigation concerned the President, and some of his actions, such as firing the FBI director, involved facially lawful acts within his Article II authority, which raises constitutional issues discussed below. At the same time, the President's position as the head of the Executive Branch provided him with unique and powerful means of influencing official proceedings, subordinate officers, and potential witnesses-all of which is relevant to a potential obstruction-of-justice analysis.

MUELLER REPORT: A preclusion of "corrupt" official action is not a major intrusion on Article II powers. For example, the proper supervision of criminal law does not demand freedom for the President to act with the intention of shielding himself from criminal punishment, avoiding financial liability, or preventing personal embarrassment. To the contrary, a statute that prohibits official action undertaken for such personal purposes furthers, rather than hinders, the impartial and evenhanded administration of the law. And the Constitution does not mandate that the President have unfettered authority to direct investigations or prosecutions, with no limits whatsoever, in order to carry out his Article II functions.

MUELLER REPORT: With respect to whether the President can be found to have obstructed justice by exercising his powers under Article II of the Constitution, we concluded that Congress has authority to prohibit a President's corrupt use of his authority in order to protect the integrity of the administration of justice.

MUELLER REPORT: ...applying obstruction-of-justice statutes to presidential conduct that does not involve the President's conduct of office-such as influencing the testimony of witnesses-is constitutionally unproblematic. The President has no more right than other citizens to impede official proceedings by corruptly influencing witness testimony. The conduct would be equally improper whether effectuated through direct efforts to produce false testimony or suppress the truth, or through the actual, threatened, or promised use of official powers to achieve the same result.

Trump's decision to fire Comey

In the interview, Barr talked about Trump's firing of Comey in May 2017, an action that was investigated by Mueller as potentially a criminal act of obstruction.

In Mueller's analysis, he said there was strong evidence that this action was related to an ongoing proceeding and there was some proof that Trump acted with corrupt intent -- two of the key elements need to prove obstruction. Barr rejected this analysis and explained in the interview that his team determined that the threshold was not reached in this case.

Barr's comments

BARR: ...let's take the again the firing of Comey. One of the elements is that you have to show that the act objectively speaking will have the probable effect of obstructing a proceeding and we don't believe that the firing of an agency head could be established as having the probable effect, objectively speaking, of sabotaging a proceeding. There was also we would have to prove corrupt intent, the report itself points out that one of the likely motivations here was the President's frustration with Comey saying something publicly and saying a different thing privately and refusing to correct the record. So that would not have been a corrupt intent. So for each of these episodes we thought long and hard about it, we looked at the facts and we didn't feel the government could establish obstruction in these cases.

Mueller's comments

MUELLER REPORT: The nexus element would be satisfied by evidence showing that a grand jury proceeding or criminal prosecution arising from an FBI investigation was objectively foreseeable and actually contemplated by the President when he terminated Comey. Several facts would be relevant to such a showing. At the time the President fired Comey, a grand jury had not begun to hear evidence related to the Russia investigation and no grand jury subpoenas had been issued. On March 20, 2017, however, Comey had announced that the FBI was investigating Russia's interference in the election, including "an assessment of whether any crimes were committed." It was widely known that the FBI, as part of the Russia investigation, was investigating the hacking of the DNC's computers-a clear criminal offense. In addition, at the time the President fired Comey, evidence indicates the President knew that Flynn was still under criminal investigation and could potentially be prosecuted, despite the President's February 14, 2017 request that Comey "let[] Flynn go." ...On March 31, 2017, the President signaled his awareness that Flynn remained in legal jeopardy by tweeting that "Mike Flynn should ask for immunity" before he agreed to provide testimony to the FBI or Congress. And in late March or early April, the President asked McFarland to pass a message to Flynn telling him that the President felt bad for him and that he should stay strong, further demonstrating the President's awareness of Flynn's criminal exposure.

MUELLER REPORT: Substantial evidence indicates that the catalyst for the President's decision to fire Comey was Comey's unwillingness to publicly state that the President was not personally under investigation, despite the President's repeated requests that Comey make such an announcement.

MUELLER REPORT: We also considered why it was important to the President that Comey announce publicly that he was not under investigation. Some evidence indicates that the President believed that the erroneous perception he was under investigation harmed his ability to manage domestic and foreign affairs, particularly in dealings with Russia... Other evidence, however, indicates that the President wanted to protect himself from an investigation into his campaign... In addition, the President had a motive to put the FBI's Russia investigation behind him.

MUELLER REPORT: Finally, the President and White House aides initially advanced a pretextual reason to the press and the public for Comey's termination... The initial reliance on a pretextual justification could support an inference that the President had concerns about providing the real reason for the firing, although the evidence does not resolve whether those concerns were personal, political, or both.

Public release of the Mueller report

Barr and Mueller are also at odds about the way the report was first presented to the public. Though Mueller this week praised Barr for releasing nearly all of the 448-page report, the two squabbled in March about the first conclusions the public would see from it.

Barr has criticized Mueller's team for not redacting the report in a way that would make it immediately releasable, while Mueller has said he prepared certain sections of the report that Barr decided not to include in his initial releases of information.

Barr's comments

BARR: Right, and so because we were not involved in the investigation we would have no way looking at the report of determining what was grand jury material and what wasn't, so we had for a period of weeks been asking the special counsel's office to highlight the stuff so we could quickly process it for release and I guess--

CRAWFORD: For a period of weeks you had asked for this material?

BARR: Yeah even before the March 5 meeting we had asked or raised the subject--

CRAWFORD: And what was the response?

BARR: And then at the March 5 meeting I made it explicit and then after the March 5th meeting we asked...

CRAWFORD: And what was the response?

BARR: We thought it was being-- we thought it was being done and I do believe they were putting in more footnotes in that would be necessary ultimately in identifying the material but whether the wires were crossed or whatever it didn't come in a form that identified the 6E material.

CRAWFORD: And that was a surprise to you when you got the report?

BARR: Yes.

CRAWFORD: It was.

BARR: And it immediately meant that you know it was going to be a period of weeks before we could get the report out if I had my druthers I would have liked to get the report out as quickly as possible.

CRAWFORD: So instead, you turned this four page summary?

BARR: Right, because I didn't think the body politic would allow us to go on radio silence for four weeks. I mean, people were camped outside my house and the department and every- there was all kinds of wild speculation going on. Former senior intelligence officials who were purporting to have it- or intimating that they had inside information were suggesting that the President and his family were going to be indicted and so forth.

Mueller's comments

MUELLER'S PRIVATE LETTER TO BARR: I previously sent you a letter dated March 25, 2019, that enclosed the introduction and executive summary for each volume of the Special Counsel's report marked with redactions to remove any information that potentially could be protected by Federal Rule of Criminal Procedure 6(e); that concerned declination decisions; or that related to a charged case. We also had marked an additional two sentences for review and have now confirmed that these sentences can be released publicly.

Accordingly, the enclosed documents are in a form that can be released to the public consistent with legal requirements and Department policies. I am requesting that you provide these materials to Congress and authorize their public release at this time.

As we stated in our meeting of March 5 and reiterated to the Department early in the afternoon of March 24, the introductions and executive summaries of our two-volume report accurately summarize this Office's work and conclusions. The summary letter the Department sent to Congress and released to the public late in the afternoon of March 24 did not fully capture the context, nature, and substance of this Office's work and conclusions. We communicated that concern to the Department on the morning of our investigation. There is now public confusion about critical aspects of the results of our investigation. This threatens to undermine a central purpose for which the Department appointed the Special Counsel: To assure full public confidence in the outcome of the investigations.

MUELLER PRESS CONFERENCE: At one point in time, I requested that certain portions of the report be released. The attorney general preferred to make that -- preferred to make the entire report public all at once. And we appreciate that the attorney general made the report largely public. And I certainly do not question the attorney general's good faith in that decision.