Germans in CK are one united group. Although Saxon get separated probably thanks to Charlemagne.There's a lot of overlap, though, given that the Crimeans speak a Kipchak language and that many steppe peoples were exogamous and prone to intermarriage. These were not homogeneous groups. And yes, you should write "Tatar," but EU uses "Tartar" so eh. Either way, it's weird that one game notes the cultural divide while CK does not.
Some idea of how Russians distinguished them can be found when looking at 1897 census data. Look at "Turkic-Tatar languages" section.It's quite hard to say were XIX century Russians even wrong, because really, should you ask XIX century Kazakh something like "What is your ethnicity?" he would probably say [clan] [tribe] [jüz] "Baltaly section of Naiman tribe, Middle jüz", or just Naiman, and then you ask Kirgiz the same question, and he answers "Boz section, Naiman tribe". And you can see that they are clearly speaking different languages, so you just pull some random word from your ass and stamp it on the map.
Well, maybe somewhere out of CK map and timeframe. The Siberian examples that you gave might be Russian influence.Anyway, I can speak about Turkic tribalism all day long, but there was some people identifying themselves as Tartars in the latter half of CK2 timeframe.
Just one interesting fact - a 1654 Italian book about Manchu conquest of Ming is called De bello Tartarico historia - "History of Tatar war".