The Byzantine Empire was the Eastern Roman empire - we really on refer to them differently for temporal convenience. The west were the Latin speakers and the east were the Greek speakers (as least for the first half-millennium). And many people still called themselves Emperor of Rome, in a continuous succession, after the fall of the west. For quite a while one of the Pope’s titles was (legitimately) Emperor of the Holy Roman Empire.
By the 20th century it was down to 3 rightful heirs, all trying to make Europe recognize them as THE Emperor. But in the mean time their empires still recognized them as such.
The Byzantine Empire was the Eastern Roman empire - we really on refer to them differently for temporal convenience. The west were the Latin speakers and the east were the Greek speakers (as least for the first half-millennium). And many people still called themselves Emperor of Rome, in a continuous succession, after the fall of the west. For quite a while one of the Pope’s titles was (legitimately) Emperor of the Holy Roman Empire.
By the 20th century it was down to 3 rightful heirs, all trying to make Europe recognize them as THE Emperor. But in the mean time their empires still recognized them as such.