I have been doing research specifically relating to Sitting Bull and his tribe's stay in Canada, and I have been having trouble wrapping my head around all the different names used. They are all Sioux, and they are all Lakota. They are also called Tetons, and Hunkpapa. I'm asking for some clarification on what the distinctions between all these monikers are, and whether they are all just different words describing the same thing. Thanks for any help!
For the benefit of those who don't check /r/AskAnthropology, I'll post my answer here as well:
There's a mix of synonyms and subdivisions here. Sioux is derived from the Ojibwe name for the Dakota-Lakota alliance they were fighting, the Očhéthi Šakówiŋ--the Seven Council Fires / Great Sioux Nation. So the breakdown looks like this. Bolded names are the seven constituent parts of the Očhéthi Šakówiŋ.
(Oceti Sakowin / Seven Council Fires / Great Sioux Nation)
#Isáŋyathi (Santee / Eastern Dakota)
#Wičhíyena (Western Dakota)
#Lakota
The Lakota oyáte (the name for the lowest tier of subdivision on this list) can be subdivided further, but since you aren't concerned with a subdivision below Hunkpapa, I didn't bother going into that. Likewise, the Dakota groups can be subdivided, but I didn't go into that for the same reason.
I suggest you try /r/AskAnthropology. You might actually get a response from someone with direct experience with the Sioux.