arena vs hippodrome

arena and hippodrome both are nouns.

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

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

arena (noun)	hippodrome (noun)
a playing field where sports events take place	a stadium for horse shows or horse races
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