Wait...aren't Kazakhs supposed to represent Kazakhstan...

You are confusing two different peoples.

Although Kazakhs are a former Soviet state, they are different from the Cossacks.

Cossacks were mounted soldiers of Russia. They are famous for riding horses and for their dancing. Think of them as Russian cowboy type archetypes.

Kazakhs too are known for their horsemanship, but they are Muslim people who look more like Mongolians or Chinese than Russian.

The word Kazakh is based on the word Cossack since the two groups were horse peoples of the former Soviet Union. That just adds to the confusion... I know!

Check out the wikipedia entries on both. This may clear up some things.