No, it's more to do with the ambiguity of the Arabic original ad-Dawlah al-Islāmiyah fī 'l-ʿIrāq wa-sh-Shām. The "Sham" bit here can be refer either to the present day state of Syria, hence ISIS; or the historical greater Syria aka Levant, hence ISIL. However, the group internally dropped the qualified some time ago, now it's just Islamic State, with the obvious implication that it's the global state for true believers.

Wikipedia goes into all this in detail: https://en.wikipedia.org/wiki/Names_of_the_Islamic_State_of_...

There was a tweet about the poor NSA intern who would be tasked with the code to identify whether "is" referred to the organization or the verb. The paranoid side of me always assumed that the rebranding to Isis could have been suggested by the Pentagon to news organizations for that reason.