History lesson needed!

I'm not an expert so anyone who knows better feel free to correct me.

Remember in those times there was not really nation-states as we have today. Especially among the steppe nomads people were divided by tribe/clan affiliation. While the Kazakhs were once united with the rest of the nomads under Genghis Khan's "Mongol Empire," that did not necessarily make them one big tribe with the rest of the people "united" under Genghis Khan.

When Genghis Khan died his empire was divided among his descendants. So in the generations after Genghis Khan the nomads were no longer united and would eventually return to warring amongst themselves. This is why even though both the Kazakhs and Jungars consider themselves descendants of Genghis Khan (because they descended from his successors), it does not mean they are the same people or make them both "Mongol."

Hope that makes sense. In a nutshell, the nomads of central Asia were once united under Genghis Khan. The empire was divided among his sons (making the people under each of these divisions technically his "descendants") and in time disintegrated back into the infighting/tribal-rivalry that was the way of life before Genghis Khan.

Again, I admit I'm not an authority on the subject so corrections are welcome.