steeplechase vs horse race

steeplechase and horse race both are nouns.

Word	Noun	Adjective	Verb	Adverb
steeplechase	Yes	No	No	No
horse race	Yes	No	No	No

As nouns, horse race is a hypernym of steeplechase; that is, horse race is a word with a broader meaning than steeplechase:

steeplechase: a horse race over an obstructed course
horse race: a contest of speed between horses; usually held for the purpose of betting

steeplechase (noun)	horse race (noun)
a horse race over an obstructed course	a contest of speed between horses; usually held for the purpose of betting
a footrace of usually 3000 meters over a closed track with hurdles and a water jump