American Indian language vs Indian

American Indian language and Indian both are nouns.

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

As nouns, American Indian language and Indian are synonyms defined as:

American Indian language and Indian: any of the languages spoken by Amerindians

American Indian language (noun)	Indian (noun)
any of the languages spoken by Amerindians	any of the languages spoken by Amerindians
	a native or inhabitant of India

American Indian language (adjective)	Indian (adjective)
	of or relating to or characteristic of India or the East Indies or their peoples or languages or cultures
	of or pertaining to Native Americans or their culture or languages