I think we're missing the point. ISIS and ISIL are both wrong. ISIS/ISIL was a group of people trying to establish an Islamist caliphate. They have successfully been running a country for the past few months, with their own courts, their own "police," and their own funding. I think they succeeded in that goal (at least for now), so they are no longer just a group of people trying to establish a caliphate. It's more correct to call them the Islamic State. They're not just the terrorist group ISIS/ISIL anymore. Not that this really even matters much. Edit: I take that back. What we call "our" enemy actually matters a lot. It's just that when media figures refuse to use the term "Islamic State," or when they say "so-called" Islamic State, it really exemplifies how in denial they are that their precious war wasn't successful.
Not that this really even matters much.
-Actually, it matters quite a lot. Its far easier to gain public support for covertly battling a "terrorist organization" with little public scrutiny or accountability. Once you are engaged in battle with an established "state," even if it's one whose legitimacy the majority of the world doesn't recognize, it becomes more "real." With "real" comes accountability, both procedurally and fiscally.
Actually, I wholeheartedly agree. I am curious, though, what you mean when you say it would matter procedurally. Do you mean when it comes to getting approval and support for fighting them, or when it comes to actually fighting them?