The Cherokee and Sioux have had little to do with one another.
The Lakota Sioux kicked the Crow out of the tall grass prairie country during their migration out of Minnesota in the early 19th Century. Most Crows these days (I’ve known a few) loathe the Sioux.
And of course the Crow drove the Shoshone out of what they now consider their homeland.
The Crow and Northern Cheyenne were traditional enemies, but a twist of fate (or someone at the Bureau of Indian Affairs who didn’t give a darn) resulted in their reservations being side-by-side in Southeastern Montana.
Even before that, the Sioux were much further east, and I think I read that in the 1600s they may actually have been very near the East Coast. I’m not sure who shoved them into Crow territory but some tribe or tribes did. Everyone thinks of them as Plains Indians but the Plains culture was relatively modern, after the reintroduction of the horse to the Americas by the Europeans.