Byzantium vs Byzantine Empire

Byzantium and Byzantine Empire both are nouns.

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

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

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

Other synonyms of Byzantium include Eastern Roman Empire.

Byzantium (noun)	Byzantine Empire (noun)
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
a continuation of the Roman Empire in the Middle East after its division in 395