football stadium vs arena

football stadium and arena both are nouns.

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

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

Other hypernyms of football stadium include athletic facility, bowl, sports stadium, stadium.

football stadium (noun)	arena (noun)
a stadium where football games are held	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