Australian state vs province

Australian state and province both are nouns.

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

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

Australian state: one of the several states constituting Australia
province: the territory occupied by one of the constituent administrative districts of a nation

Other hypernyms of Australian state include state.

Australian state (noun)	province (noun)
one of the several states constituting Australia	the territory occupied by one of the constituent administrative districts of a nation
	the proper sphere or extent of your activities