Asian American vs American

Asian American and American both are nouns.

Word	Noun	Adjective	Verb	Adverb
Asian American	Yes	No	No	No
American	Yes	Yes	No	No

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

Asian American (noun)	American (noun)
an American who is of Asian descent	the English language as used in the United States
	a native or inhabitant of the United States
	a native or inhabitant of a North American or Central American or South American country

Asian American (adjective)	American (adjective)
	of or relating to or characteristic of the continents and islands of the Americas
	of or relating to the United States of America or its people or language or culture