Their is an issue with how you are thinking about this. One must remember first that the term byzantine is a modern construct. The people we call Byzantines were in contemporary terms were Romans and referred to themselves as such. The population of Byzantium was made up of people from many different regions and ethnicities. Over time these people would assimilate to and also alter byzantine culture. With that said, once grafted into Byzantine society through civil service (governmental or militarily), they would become "Roman." This same interaction happened after the fall of the Byzantine empire under. People will adjust and assimilate if they are not: killed, enslaved, or flee to other regions. Many of the Byzantine thema switched sides some-what frequently in the name of either power or survival during the Byzantine period. The proximity of Greece did play a significant role in the adoption of Greek as the imperial language over Latin. This did not detract though their feeling that they are roman. So for the most part the "Byzantine Greeks" are not what we call Citizens of turkey and the Byzantine Greeks that lived in Greece are now what we call Greek.

The Byzantine empire had a larger population, but don't forget that in the early centuries, it encompassed the area today occypied by countries in the Balkans, Greece, Turkey, the Near East and north Africa. In the later centuries, the Empire shrunk down to encompass mainly Greek-speaking, Eastern Orthodox populations (having lost territories and population to the Arabs, the Latins and the Ottomans). Another reason for population loss during the Ottoman period is conversion (forced or willing), losing children to the devshirme system, and emigration to other European countries, especially Italy, Corsica, central Europe and the Hapsburg-held part of the Balkans. Also note that many Greeks from Asia Minor emigrated to North America after the population exchange in 1922.