How was the Roman Empired called in western Europe...

...during the Middle Ages?

Roman Empire? Bizanthium? Greeks? Something else?

And how did (Eastern) Romans called westerners? Franks? Latins?
 
I think the popular term was "Grifon" ie Greek. In diplomatic correspondence the Emperor might have been called "Empeor of Constantinople". Iirc, "Byzantine" was an academic term adopted by Western historians in a much later period.

For vice versa, either "Franks" or possibly "Lombatds". Toynbee recounts a visit by an ambassador from the Western Empire, about the mid-10C who took umbrage at his countrymen being called "Lombards".
 
Reading the accounts of Anna Commnena and Geoffrey of Villehardouin, the most comon terms were:

Western terms for the East: Greeks, Emperor of Constantinople, Eastern Empire, Orientals.

Eastern terms for the West: Latins, Franks, Lombards, Italians.
 
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