Bernie Sanders may be a democratic socialist, but after he announced his run for the Democratic presidential nomination earlier this year, frontrunner Hillary Clinton was eager to stress what they agreed on:

I agree with Bernie. Focus must be on helping America's middle class. GOP would hold them back. I welcome him to the race. –H — Hillary Clinton (@HillaryClinton) April 30, 2015

But while Clinton and Sanders may be using somewhat similar rhetoric these days, the differences between them on economics remain vast. Sanders wants his party to challenge the power of the wealthy and corporations far more directly, both rhetorically and substantively. But Clinton would rather turn them into allies — mobilizing support from the 1 percent, rather than demonizing them.

Now, keep in mind that despite the current turmoil in the House of Representatives, it's generally expected to remain in Republican hands for quite some time — so when it comes to actual legislation, a Democratic president's strategic approach to Congress and executive power might actually matter more than which specific new laws he or she wants.

But on some issues, like trade and foreign policy, the president has broad authority to take the initiative. And it's clear that there, President Sanders and Clinton would act in very different ways.

1) Money: Sanders attacks the rich; Clinton wants to raise money from them

Clinton wants to win the support of the wealthy and corporations to her side. Sanders wants to attack them and try to break their power. As Dylan Matthews wrote, the top organizations whose employees give to Sanders are overwhelmingly unions — while for Clinton they're mostly banks and corporations. That fundamental difference in approach would almost certainly continue on from their campaigns to their administrations.

From Bill's campaigns and presidential fundraising to Hillary's campaigns to their foundation's fundraising, it's clear the Clintons have a deep ingrained sense of how important money is. The generous interpretation of this is that they respect this power and want to harness it to advance their party's goals, and to prevent Republicans from gaining power. The more critical interpretation is that they mainly want to advance themselves — and are willing to carry water for corporate and wealthy interests in order to do this.

Over the past year, Clinton has spoken about how too much income and wealth are going to the very richest, warning that "extreme inequality" can corrupt societies. Earlier this year, she complained in Iowa that the taxes of hedge fund moguls were too low. But according to a report by Politico, "The hedge fund managers who’ve long been part of her political and fundraising networks aren’t sweating the putdown and aren’t worrying about their take-home pay just yet." And the New York Times reported last year that Clinton was exploring, through discussions with donors and friends in business, how her campaign can address inequality "without alienating businesses or castigating the wealthy."

Sanders, meanwhile, has no interest in soliciting funds from the richest of the rich — and would likely have no success at it, considering how often he attacks them. Back when he was mayor of Burlington, Vermont, Sanders did eventually develop a productive working relationship with the area's economic powerhouses, as I documented in my profile of Sanders. But it's difficult to imagine something similar happening on the national level — and Sanders himself doesn't expect it. Last year, he said that if he were president, he expected the billionaire Koch brothers would be "running ads 24 hours a day, seven days a week, trying to destroy me and my family and everything else we believe in." If you thought the business community's resistance to Obama was impressive, you ain't seen nothing yet.

WATCH: 'How wealth inequality is dangerous for America'

2) Trade: Sanders is extremely skeptical of new agreements, while Clinton has waffled

Trade is an issue on which the personal preferences of the president make a huge difference, regardless of who controls Congress. Since trade agreements are negotiated by the executive branch, a president can either choose to pursue new ones, or put them on hold entirely.

It's also one of the issues where the contrast between Sanders and Clinton may be the clearest. "Unfettered free trade has been a disaster for the American people," Sanders told me last year. He views the Democrats' support of trade deals like NAFTA as one of the key reasons they've lost support among the white working class. He said that during his two and a half decades in Congress, "I voted against all the trade agreements." And he's been harshly critical of the Trans-Pacific Partnership, and is making his opposition to it a key feature of his campaign.

But much like President Obama, Clinton appears to be supportive of most trade deals unless a primary is approaching. NPR's Domenico Montanaro charts the changes in her rhetoric and positions over time. In 2000, NAFTA was "flawed." In 2004, it was "good for New York and America." In 2008, it had "not lived up to its promises." Clinton similarly shifted on the Trans-Pacific Partnership, bragging in 2012 that it was the "gold standard in trade agreements," but coming out in opposition to it this month.

3) Foreign policy: Clinton is more of a hawk than Sanders — and most other Democrats

On foreign policy issues involving the use of American force abroad, it's actually Clinton, not Sanders, who's most out of step with the Democratic Party. And since the president has broad authority to conduct foreign policy without Congressional oversight, this matters quite a bit. "It's very clear that a President Clinton would bring far more hawkish instincts to bear on global problems than the current president — or, for that matter, your average Democratic voter," Zack Beauchamp wrote earlier this year.

This isn't just about Clinton's long-ago vote for the Iraq War. Throughout Clinton's service in the Obama administration, she consistently took a more hawkish line than the president. In 2009, she pushed hard for a surge of troops to Afghanistan, as Obama remained undecided for months. In 2011, she strongly advocated for action against Qaddafi's regime in Libya, and Obama eventually came to agree. In 2012, she wanted to arm the rebels against Assad's regime in Syria, but Obama turned down her entreaties. And earlier this month, she called for a no-fly-zone in Syria.

As for Sanders, while he voted against the Iraq War and wants cuts in defense spending, he isn't a total far-left peacenik on foreign policy. He voices sympathy with Israel's security concerns and warns of the dangers of ISIS — positions that have sometimes led to awkward confrontations with his more radical constituents. But unlike Clinton, he's an instinctive critic of most large-scale military interventions abroad, saying they are frequently expensive and counterproductive. "ISIS is a brutal, awful, dangerous army and they have got to be defeated," he said last year. And yet, he added, "this is not just an American problem," and called on Arab nations to take the lead in the fight.

4) Health reform: Sanders wants single-payer — but likely couldn't get it through Congress

Clinton and Sanders have long both been interested in health care — and have long advocated for dramatically different plans. But as long as the Republicans hold onto the House, it's not clear how much those differences will matter.

Sanders sticks to his socialist roots by supporting a single-payer system — "Medicare for all," he calls it. Obamacare, he said last year, was a "modest step forward," but argues it doesn't do enough to expand coverage and make it affordable. In the current system, he said, "the goal is for the insurance companies and the drug companies to make as much money as possible." When Vermont moved toward its own single-payer system Sanders was thrilled — but since then, the plan has been indefinitely postponed due to cost concerns.

Clinton said earlier this year that she wants to build on "what works" in Obamacare — the basic framework of which was very similar to her 2008 campaign's health reform proposal. Notably, she said back then that over her 15 years of work on the issue, "I never seriously considered a single-payer system." Her reasons were pragmatic. "Talking about single-payer really is a conversation ender for most Americans, because then they become very nervous about socialized medicine," she's said.

In 2008, Clinton did support one key proposal that never became law — a public option to let people choose government-provided insurance. And she suggested that if it was popular, it could lead to a more extensive overhaul of the system. "Let Americans choose. And what better way to determine that than letting the market have some competition and, you know, see where it does lead to," she said.

Clinton's belief that single-payer had no chance of getting through even a Democratic Congress (let alone a Republican one) is very widely shared in Washington. Indeed, Sanders would likely agree with her. To pass broad policy changes like single payer, he believes, we need a "political revolution" in this country that would elect a very different Congress. Still, it's clear that Sanders would loudly and consistently advocate for single-payer, attempting to build support for it.

5) Spending: Sanders wants big spending

Most Democrats would love to increase federal spending on their favorite policy priorities. But mainstream politicians in the party have recently tended to embrace messaging about fiscal discipline. Clinton — wary of being tarred as a big-spending Democrat, like her husband was in the beginning of his administration — is one of them, generally proposing that increases in spending would be paid for by other spending cuts or tax hikes.

Not Sanders. His speeches are filled with calls for dramatic increases in government spending. Pay for the first two years of college at any public university! Spend $1 trillion on infrastructure! Move to single-payer health care!

Overall, he downplays the deficit as a problem, as his appointment of Stephanie Kelton as the top Democratic economist on the budget committee shows. "She thinks that, in many cases, government surpluses are actively destructive and balancing the budget is very dangerous," writes Dylan Matthews. When Sanders does discuss pay-fors, he talks about cutting defense or hiking taxes on the wealthy (not the middle class).

As on health care, though, the differences here might not matter that much in the end. Congress tends not to support big new liberal spending programs — either because the taxes require to fund them are too high, because they don't want to increase the deficit too much, or because they prefer to increase the deficit in other ways.

Notably, this is why Vermont's single-payer plan was tanked. The state only funded $2.7 billion worth of programs in taxes each year, but it ended up needing $2.5 billion more for single-payer. As Sarah Kliff reported, they couldn't come up with the money — the tax increase required to enact it would have been gigantic — so they scrapped the plan.

6) Clinton has more frequently pushed for gun control measures

One major issue on which Clinton has a more consistently liberal record than Sanders is gun control. Representing rural Vermont, Sanders has frequently voted against Democrats' efforts to restrict gun sales in Congress. For instance in the early 1990s, he opposed many versions of the Brady bill (which created background checks and a waiting period for gun purchases), arguing then that gun control shouldn't be a federal concern. He also voted for a 2005 law that made it much harder to sue gun manufacturers.

However, Sanders has voted for other gun control measures, such as the Democrats' post-Newtown gun control bill to expand background checks and restore the assault weapons ban. He said then that there was "a growing consensus" that "we have got to do as much as we can to end the cold-blooded mass murders of innocent people." His campaign is currently working on a plan to address gun violence.

Hillary Clinton, meanwhile, has usually pushed for tougher gun control measures when the issue has come up, as you can see in a rundown from Reason's Jacob Sullum here. For instance, in May 2014 she argued that "we've got to rein in what has become almost an article of faith that almost anybody can have a gun anywhere at any time." And earlier this month, Clinton proposed an ambitious series of executive actions on guns, including going around Congress to close the "gun show loophole." However, when she was fighting for red-state votes during the 2008 presidential campaign, she tended to emphasize her support of the Second Amendment, and stressed that the federal government shouldn't have "blanket rules that they're going to try to impose."