arena vs bullring

arena and bullring both are nouns.

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

As nouns, bullring is a hyponym of arena; that is, bullring is a word with a more specific, narrower meaning than arena:

arena (noun)	bullring (noun)
a playing field where sports events take place	a stadium where bullfights 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