province vs arena

province and arena both are nouns.

Word	Noun	Adjective	Verb	Adverb
province	Yes	No	No	No
arena	Yes	No	No	No

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

Other hypernyms of province include area, domain, field, orbit, sphere.

province (noun)	arena (noun)
the territory occupied by one of the constituent administrative districts of a nation	a playing field where sports events take place
the proper sphere or extent of your activities	a large structure for open-air sports or entertainments
	the central area of an ancient Roman amphitheater where contests and spectacles were held; especially an area that was strewn with sand
	a particular environment or walk of life