How did the byzantine empire differ from the roman empire?

The Byzantine Empire was the Eastern Roman Empire after the split. The two halves of the empire both celebrated Christianity but had differing opinions on some topics, including the Pope. Eventually, the Pope excommunicated or kicked out, the arch bishop of Constantinople. The Byzantine Empire split and became the Eastern Orthodox Church.  

The Byzantine empire was centered in Constantinople (now Istanbul) and spoke Greek while the Roman Empire spoke Latin and was centered in Rome.  

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