stadium vs arena

stadium and arena both are nouns.

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

As nouns, stadium and arena are synonyms defined as:

stadium and arena: a large structure for open-air sports or entertainments

Other synonyms of stadium include bowl, sports stadium.

stadium (noun)	arena (noun)
a large structure for open-air sports or entertainments	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