American state vs province

American state and province both are nouns.

Word	Noun	Adjective	Verb	Adverb
American state	Yes	No	No	No
province	Yes	No	No	No

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

American state: one of the 50 states of the United States
province: the territory occupied by one of the constituent administrative districts of a nation

Other hypernyms of American state include state.

American state (noun)	province (noun)
one of the 50 states of the United States	the territory occupied by one of the constituent administrative districts of a nation
	the proper sphere or extent of your activities