Maya vs American Indian

Maya and American Indian both are nouns.

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

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

Maya (noun)	American Indian (noun)
a family of American Indian languages spoken by Mayas	any of the languages spoken by Amerindians
an ethnic minority speaking Mayan languages and living in Yucatan and adjacent areas
a member of an American Indian people of Yucatan and Belize and Guatemala who had a culture (which reached its peak between AD 300 and 900) characterized by outstanding architecture and pottery and astronomy