covered stadium vs arena

covered stadium and arena both are nouns.

Word	Noun	Adjective	Verb	Adverb
covered stadium	Yes	No	No	No
arena	Yes	No	No	No

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

Other hypernyms of covered stadium include bowl, sports stadium, stadium.

covered stadium (noun)	arena (noun)
a stadium that has a roof	a playing field where sports events take place
	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