Timur, Turkish... Hmmm... I seem to recall something about his mother was Turkish and his father Mongol. Well at least he was mixed at a relatively short distance.
And just because he fought Mongols didn't mean he wasn't one. As noted earlier Kublai had no trouble fighting other Mongols.

The Chinese had actually learned very well. They had learned that it is hard to fight the nomads, but it is 'easy' to absorb them. 'We are far more than them, they will vanish soon'. And it worked well until the Mongols of course. The wall helped with the small raids and kept a check on the trade.
The Russians had learned how to fight the nomads, and so had the Caucasian peoples, but they hadn't learned to fight determined and superb armies like those of the Mongols. That is what set them apart. The style itself was countered, but add to it great tactics and discipline and it throws it all into confusion.