I did not know the answer until I pursued it this morning.
The following does explain the difference and THAT is the point of this thread. Not the speculation of who uses which one or why.
‘ISIS’ vs. ‘ISIL’ vs. ‘Islamic State’: The political importance of a much-debated acronym - The Washington Post
Once clarified, the distinction between the two does beg or raise a question, is there a reason for using one or the other or not.