It's one of those "depends on who you ask" or "depends on who you call a Sioux" type things. I couldn't care less personally, this is not the case for all. There is no Sioux tribe so I actually find it humorous, but that's me.

There are several tribes under the Sioux name, which is a federal designation and not a name or label any of the Sioux Nation's individual tribes gave themselves, rather it was a nickname assigned by a rival tribe and without getting into the history of that or the word, the word itself basically means "little snake" or something to that affect (I honestly don't know specifically, it's not a word in the Lakota language).

Now, this is NOT what it means these days as far as the federal classifications and even Tribal ID's use this name (in conjuction with more specific designators) as do federal documents and is not intended as derogatory, however. some tribal members take offense to it for various reasons and this is the only reason I mention it.

You wouldn't want to just call someone "sioux" unless referring to the context of the federal recognation, but honestly it's like splitting hairs. We never call ourselves "Sioux" even in the context unless it's specifically about that, we call ourselves Lakota, but often we concede to being called Sioux to non-Indians because most people know Sioux, but not necessarily Lakota. I've called people Sioux when I do't know what tribe they are from.

I also would not worry about it, those who care will correct you if you call them Sioux and they want to be referred to properly (not always however, sometimes they may take offense and say nothing). The nicest thing you can do is simply ask anyone you know as Sioux, what they prefer, because that's what it really comes down to.

At the end of the day, all "Sioux" have to refer to themselves as "Sioux" at some point in their lives, so it's technically accurate, however, there is no "Sioux" tribe and their are no "Sioux" Indians, there are many tribes, like the two you mentioned, that combined under the "Sioux" nation and I think the assumption that there is a "Sioux" tribe is what often annoys some people since the cultures are different amongst the tribes and that does matter.

For example, the "black hills" are sacred to my tibe, but not to all Sioux.

Anyways, I do appreciate you asking, people rarely care enough to even bother with it.