Present day Turkey was a land of many great nations. There were Hittites, Armenians, Lydians, Celts (Galatians), Syrians, Medes (Kurds), Persians and of course Greeks. Real Turks invaded the area around A.D 1000 as a small, but determined band of warriors. They eventually conquered all middle East, North Africa and Balkans. The people were forced to convert to Turkish nationality and Muslim faith.
In the population exchange in the 1920s, Muslims in Greece were considered Turks and Greek Orthodox in Turkey were considered Greeks (even if they spoke Turkish).
In the late Middle Ages/early modern period, a lot of Albanians moved south into Greece and many rural areas were still Albanian-speaking in the 19th or even the 20th century. Of course the policy of the government was to get everyone to speak Greek.
In 1980 I spent a few days in a village in central Greece with several other Americans. One of the Americans told me of a conversation she had with an old lady in the village. After they exchanged greetings in Modern Greek, the old lady told her, "That's all the Greek I know. Do you speak Albanian?"
The Biblical Galatians in Turkey had their origins as Gallic/Celtic nomads and mercenaries from western and central Europe.