Check out the below link. It quite a good read. It explains that the Turks and Greeks although are not completely related, but come from the same area (present day Ethiopia)which suggests that they have alot similarities. Its a scientific DNA research that was conducted in spain.
Not true at all.
The Turks who invaded Anatolia were Ghuzz Turks.
The Bulghars who invaded the Danube plane in the 7th Century where Kok-Turks.
In the late 6th century the Proto-Bulghars and related tribes called the Q'azars broke from the Western Turkish Khaganate. The Q'azars and the Bulghars fought along a region around the Aral and Caspian seas called Trans-Oxiana. The Bulghars were defeated and split in two. One group settled the Volga River valley near the intersection with the Kama river. The Volga Bulghars survive today, still speaking Chuvash.
The other Bulghar's were pushed by other Turkish groups West along the Black Sea and into the Balkans. Being a relatively small people, the Bulghars quickly mixed with their subject Slavic and Thracic peoples in the Danube plain. The souther Bulghars adopted Christianity and emulated Byzantium. They droped the dual Khan/Khagan system of governance and took up that of the Byzantines.
Check out the history of the Proto-Bulgharians.
http://members.tripod.com/~Groznijat/p_bulgar/index.htm
The Ghuzz Turks settled the area between the Oxus river and along the Caspian sea in the 7th century. These Turks were At-Turks and spoke a different language. It was this groyups that swept the middle east under the Seljuk and then under the reign of the Osmani dyunasty conquered the Byzantine Empire.
Thus Bulgarians and Turks have some mixed history even before the Ottomans (Osmani) conquered Constantinople in 1454. I have met some persians that appear to have slightly oriental facial features, but never a turk that appears this way. So apparently the turkish peoples have changed alot over the centuries.