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_...