What I'm saying is, stick to the known and proven facts
Definition of Tatar will change depending on where you live in. If you live in Turkey, Tatar will be understood differently. Elsewhere, will be understood differently. In Russia, it is Muslim Mongols, similar to West sources. If you ask a panturkist professor, he will prove you all Tatars including Poland, Lithuanian, Finland tatars are Turkic. And, this theory will be objected by an anti-panturkist one. Main reason for Tatars being seperated from other Tatars is due to they used different languages and writing languages depending on where they have lived. For such things, find a very old person, especially a very old woman in a village who never went to school. Listen to her carefully. Since her language will carry 'tongueprints' of very old past, you can find the true history, true native language of Tatars. When I was talking with my grandmother (never went out of village) I learnt many words that nobody knows in today Turkey. Interestingly, I heard similar words from a Romanian (gagauze(gokoghuz) Turk last year. My highly educated Turkish fellow didnt understand him, but, I understood. So, languages written and spoken may confuse you as written things have been influenced due to politics. To understand who the Polish Tatars are, you need to find such a person and let her say some basic words like 'i, you, he/she/it, water, air, bread, mother, father, etc.' and check if they are similar to Turkic or Mongol.
Words in Polish may mislead you as many Turkic words (during Ottoman empire) entered Polish.
Here is a document written in 1924 written by a Polish of the day (given on Poland embassy in Ankara.)
ankara.polemb.net/index.php?document=197Polonya, Türkiye ile sadece politik ilişkilerde bulunmayıp, ticari ilişkilere de girişmiş; Türkiye'den Polonya'ya çeşitli kumaş, halı, silah, eyer, yün, tütün, meyve ve mücevher gibi şeyler gelmiş ve bu ilişki yüzünden pek çok kimsenin bilmediği Türkçe kelimeler Polonya diline geçmiştir. Kar, kazak, karabela, kuntuş, kalem, pantolon, fasulye, yatağan, fincan, kestane ve benzeri...
Basically paragraph says: Poland and Turkey had not had only political relations, but, also trade relations (for centuries.) Traders brought many items such as textile, carpet, riffles, horse saddles, wool, tobacco, fruits, jewellery, etc. and because of these, some words that many dont know entered Polish language. Kar (profit), kazak (a kind of man cloth), karabela (ottomanish word. kara=black in turkish and bela=wrangler in arabic), kuntus = a kind of man cloth (kontos = a kind of woman cloth), kalem (ottomanish, arabic origin = pencil), fasulye = bean, yatagan = a kind of sword, fincan = coffee/tea cup, kestane = chestnut, etc etc. If you hear such words from Polish Tatars, you may think they are Mongol origin. Some of them are not even Turkic, but, Ottomanish (mixture of Turkic, Persian and Arabic as seen in "karabela" above.)