In his Nobel Peace Prize acceptance speech four-and-half years ago, when the United States was still fighting George W Bush's battles against al-Qaida, Barack Obama spoke not so much about peace as the necessity of sometimes going to war. "Evil does exist in the world," Obama remarked. "A nonviolent movement could not have halted Hitler's armies. Negotiations cannot convince al-Qaida's leaders to lay down their arms."

Seemingly out of nowhere, that pragmatic vision of the world has now turned back to Iraq. A well-organized and blood-thirsty group of insurgents, Islamic State in Iraq and the Levant (Isis), is on the march. They may soon be headed for Baghdad. The Iraq government has now officially requested the United States to engage in airstrikes to stave off the militants' advance, and the US military is considering whether it has sufficient intelligence to carry out effective drone and other air operations.

In the meantime, the Pentagon appears to be quickly gathering the information it needs "to gain clarity" for what the White House has termed "the days to come" as Secretary of State John Kerry says "nothing is off the table" – all while Senate majority leader Harry Reid insists "there has been sufficient authorization" for an air campaign. After a meeting with Congressional leadership on Wednesday afternoon, Senate minority leader Mitch McConnell said the president "didn't feel he had any need for authority from us".

But if President Obama wants to start a brand-new war, he will need prior approval from Congress to fight a brand-new enemy – and he'll need to mull his decision out in the open. Because Congress hasn't given a green light for Iraq 3.0. And justifying a new war on the basis of a false link to al-Qaida would amount to just that – a redux of the Bush administration's disastrous Global War on Terror. It would also overlook the hugely different array of forces, including local tribes in Iraq helping Isis, which could make this new war even worse than it already is.

New war, you ask? Hasn't the United States already decided to use the military option to counter al-Qaida, and isn't the threat posed by Isis just a new version of the battle that Congress already authorized Bush and Obama to fight? The answer – contrary to what many have suggested – is very clearly no.

Sending drones to fight Isis isn't simply some new front on a disappearing border. Congress has only authorized, in the wake of 9/11 and before Reaper drones were even introduced, the use of force against al-Qaida – and potentially groups working in direct association with it. But Isis is very clearly not one of them.

If you read some news reports, you'd be forgiven for thinking that Isis and al-Qaida are essentially one in the same. The Wall Street Journal informed its readers when the "Al Qaeda-Linked Militants" seized control of Iraq's second largest city. The Washington Post wrote about how "Al-Qaeda renegades" seized another major town this past weekend. CNN told its audience that members of the Senate panel that held hearings on Wednesday were concerned that "al Qaeda-affiliated Islamists" will establish a beachhead in Iraq.

Those misleading connections, it seems, came largely from the Obama administration itself: the US State Department called Isis "a branch of al-Qa'ida" and "a common enemy of the United States and the Republic of Iraq" late last year, and outlets like the New York Times repeated that frame of analysis without questioning it. The administration had an opportunity to set the record straight in early 2014 when a senior administration official testified in public hearings before Congress. The title of his prepared testimony: "Al-Qaeda's Resurgence in Iraq: A Threat to US Interests" – and then he spoke about Isis "flying the black flag of al-Qaida".

But if you ask legal scholars and independent terrorism experts, you find a completely different reality – one that should give Obama pause before acting on any air strikes, even if the time to send in the drones is running short. Because there is minimizing civilian casualties before Isis reaches Baghdad, and then there is rushing into war with a public so badly misinformed by parts of the media and its own government.

On various legal blogs, academics such as Deborah Pearlstein and Jennifer Daskal have been at pains to show how Isis is not associated with al-Qaida – far from it. Fissures grew between the two groups last year when Isis "repeatedly refused" instructions and advice from the head of al-Qaida, Ayman al-Zawahiri, and outright opposed his goals and directives. This year, Zawahiri officially gave up and announced that al-Qaida would have nothing to do with Isis. Al-Qaida's senior leadership stated that it has "no connection" with Isis, and that Isis is "not an affiliate with the al-Qaida group and has no organizational relation with it."

So what about that black flag? As Professor Pearlstein notes:

[T]errorist experts have regularly pointed out the popularity of the black flag with the white lettering among a range of Islamist groups across the region.

Of course, most Americans don't read legal blogs or research reports. Most Americans believe what they see on cable news. But the American public needs to understand from President Obama the choices ahead – and the enemy we are now apparently prepared to fight. And the president shouldn't just consult Congress on this one. He needs to receive our backing, too.