Tibetan, as a lanuage has a strong tie with Chinese language, both belong to the Sino-tibetan language family, this langauge family only has two language branches, one is Chinese, the other includes Tibetan and Burmese. As an ethnic group, Tibetan has the most strong genetic or blood connection with Han-Chinese. It is estimated that Han-Chinese and Tibetan separated into two independent ethnic groups less than 6,000 year ago.
As for mongolian language, it belongs to a different language family, Altaic, however, it is a language family under argument, a few researchers believe it belongs to a language branch under Turkic language family. As for culture connection. Before the mongolian empire rose, Chinese history books gave different names for those northern neighbored nomads, Huns, Serbi, Turks and Mongolian.
It was not occupied by China, we have much more strong connection in the history than Turkish and Kurd.
When the ethnic group, Uighur, not formed, Han-Chinese has been active in Xinjiang for more than 1000 years!
This thread not about Uighur, sell your unqualified history in other place, please.
They are being occupied by China. Mongolian, Tibetan, Uighur are separate people with their own history and language. The origin and language tree is completely different. Tibet and (east-Turkistan) Uighur are occupied in 50'ies until today.