trotting horse vs race horse

trotting horse and race horse both are nouns.

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

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

trotting horse: a horse trained to trot; especially a horse trained for harness racing
race horse: a horse bred for racing

Other hypernyms of trotting horse include bangtail, racehorse.

trotting horse (noun)	race horse (noun)
a horse trained to trot; especially a horse trained for harness racing	a horse bred for racing