Athapaskan vs American Indian

Athapaskan and American Indian both are nouns.

Word	Noun	Adjective	Verb	Adverb
Athapaskan	Yes	No	No	No
American Indian	Yes	No	No	No

As nouns, American Indian is a hypernym of Athapaskan; that is, American Indian is a word with a broader meaning than Athapaskan:

Athapaskan: a group of Amerindian languages (the name coined by an American anthropologist, Edward Sapir)
American Indian: any of the languages spoken by Amerindians

Athapaskan (noun)	American Indian (noun)
a group of Amerindian languages (the name coined by an American anthropologist, Edward Sapir)	any of the languages spoken by Amerindians
a member of any of the North American Indian groups speaking an Athapaskan language and living in the subarctic regions of western Canada and central Alaska