The Huns, the Tatars, the Hungarians, the Mongols, and the Turks; are all names of the same peoples who inhabited the plains stretching from north of the Caucuses to the end of Mongolia. For the first few thousand years of recorded history, theirs is that of invading Slavic, Germanic and Chinese lands. Remember Attila the Hun?
For Western and South Asia we were protected by the mountains of the Himalayas, Persia and Armenia, as well as the Caspian Sea. This changed with the birth of Genghis Khan, who crossed the great mountains and sea. He arrived in the Muslim world at a historic moment. The Arab dynasties were at their end, exasperated by 300 years of European Crusades. At first, Arabs fought the invading hordes, the memories of the sacking of Baghdad, Aleppo and Damascus, made sure the proto-Turks were rejected from our region.
But when the Mongols converted to Islam and fought the crusaders in Palestine, Syria, the locals excepted them over. This also allowed for the 600 years of Ottoman rule that followed, and the settler colonization of Anatolia by Turkic tribes and the expulsion/defeat of the Byzantine empire that was mainly populated by Greeks and Armenians.
So, geographically, no such thing as Turkey exists, nor are any historic Turkish claims to any lands west of the Caspian Sea exists. Saying the word Turkey, is as fictitious as saying the word Saudi; both don't exist except if you accept the colonial paradigm offered.
This is one of the few historic threads you have to understand when following the issues of the Arabic world, Palestine and Syria. For a matter of fact, this is a thread that you need to follow if you want to understand Russia, China, India, all of Asia and Eastern Europe.