Definitions from Free Dictionary, Dictionary.com, and Oxford dictionary (subscriber only) should tell you the official definition.

The Roman Republic and Byzantine Empire are different because of religion, geographical location, population, language and customs. Although the Byzantine did consider themselves the hires of the Roman Empire. In the same way that the Holy Roman Empire is not the same as the Roman Empire in religion, location, language, population, and customs but again a lineage was claimed.

Definitions from Free Dictionary, Dictionary.com, and Oxford dictionary (subscriber only) should tell you the official definition.

The Roman Republic and Byzantine Empire are different because of religion, geographical location, population, language and customs. Although the Byzantine did consider themselves the heirs of the Roman Empire. In the same way that the Holy Roman Empire is not the same as the Roman Empire in religion, location, language, population, and customs but again a lineage was claimed.

This definition is all you should need. There are plenty others but mostly paraphrase this one.

The Roman Republic and Byzantine Empire are different because of religion, geographical location, population, language and customs. Although the Byzantine did consider themselves the hires of the Roman Empire. In the same way that the Holy Roman Empire is not the same as the Roman Empire in religion, location, language, population, and customs but again a lineage was claimed.

Definitions from Free Dictionary, Dictionary.com, and Oxford dictionary (subscriber only) should tell you the official definition.

The Roman Republic and Byzantine Empire are different because of religion, geographical location, population, language and customs. Although the Byzantine did consider themselves the hires of the Roman Empire. In the same way that the Holy Roman Empire is not the same as the Roman Empire in religion, location, language, population, and customs but again a lineage was claimed.