Byzantine Empire vs Byzantium

Byzantine Empire and Byzantium both are nouns.

Word	Noun	Adjective	Verb	Adverb
Byzantine Empire	Yes	No	No	No
Byzantium	Yes	No	No	No

As nouns, Byzantine Empire and Byzantium are synonyms defined as:

Byzantine Empire and Byzantium: a continuation of the Roman Empire in the Middle East after its division in 395

Other synonyms of Byzantine Empire include Eastern Roman Empire.

Byzantine Empire (noun)	Byzantium (noun)
a continuation of the Roman Empire in the Middle East after its division in 395	an ancient city on the Bosporus founded by the Greeks; site of modern Istanbul; in 330 Constantine I rebuilt the city and called it Constantinople and made it his capital
	a continuation of the Roman Empire in the Middle East after its division in 395