As far as my understanding is, the Byzantine Empire as we know it today was known by contemporaries as the Roman Empire. When did this distinction arise? Why?
I'm not sure whether there is a definitive answer but this thread and comment from /u/Tiako may help: https://www.reddit.com/r/AskHistorians/comments/14oins/at_what_point_did_the_eastern_roman_empire_become/c7f2ago/