Difference is that the US would actually be intervening at the behest of the government there. Nobody would denounce it as a violation of Iraq's territorial integrity.
These are all semantics, this is the same government that was installed as a result of US invasion. If the United States sends troops to any crisis zone, Russia will use it as a pretext to do their own peacekeeping mission. You will not defeat ISIS anyway, they will use guerilla warfare and are prepared to fight for decades if need be. Is the US public ready to sacrifice a few more trillions, thousands of lives and a possible Russian response within their sphere of influence?