Turkish People = people descended from Turks of the Ottoman Empire, now most of them are living in Turkey
Turkology = Turkology (Turcology, Turkologie) is a complex of humanities sciences studying languages, history, literature, folklore, culture, and ethnology of people speaking Turkic languages and Turkic peoples in chronological and comparative context. This includes ethnic groups from the Sakha in East Siberia to the Balkan Turks and Gagauz in Moldova.
Turkestan, spelled also as Turkistan = (Persian: ترکستان) literally meaning "Land of the Turks". The term Turkestan is of Persian origin and has never been in use to denote a single nation. It was first used by Persian geographers to describe the place of Turkish peoples. After Persia had been considerably weakened by its defeat in 1860, Imperial Russia stepped up its campaign to wrest full control over the Central Asian region from Persian dominance and on their way southward, the Russians took the city of Turkestan (in present day Kazakhstan) in 1864, mistaking its name for that of the entire region, they adopted the appellation of "Turkestan" for their new territory.
Tartary or Great Tartary (Latin: Tataria or Tataria Magna) was a name used by Europeans from the Middle Ages until the twentieth century to designate a great tract of northern and central Asia stretching from the Caspian Sea and the Ural Mountains to the Pacific Ocean inhabited by Turkic and Mongol peoples of the Mongol Empire who were generically referred to as "Tartars", i.e. Tatars. It incorporated the current areas of Siberia, Turkestan (including East Turkestan), Greater Mongolia, Manchuria, and sometimes Tibet.
Tartary was often divided into sections with prefixes denoting the name of the ruling power or the geographical location. Thus, western Siberia was Muscovite or Russian Tartary, eastern Turkestan (later Chinese Xinjiang) and Mongolia were Chinese or Cathay Tartary, western Turkestan (later Russian Turkestan) was known as Independent Tartary, and Manchuria was East Tartary.
In 2011 Tartary is quite the archaic term and Not the modern State of Tatarstan.