steeplechase vs foot race

steeplechase and foot race both are nouns.

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

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

steeplechase: a footrace of usually 3000 meters over a closed track with hurdles and a water jump
foot race: a race run on foot

Other hypernyms of steeplechase include footrace, run.

steeplechase (noun)	foot race (noun)
a horse race over an obstructed course	a race run on foot
a footrace of usually 3000 meters over a closed track with hurdles and a water jump