horse vs racehorse

horse and racehorse both are nouns.

Word	Noun	Adjective	Verb	Adverb
horse	Yes	No	Yes	No
racehorse	Yes	No	No	No

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

horse: solid-hoofed herbivorous quadruped domesticated since prehistoric times
racehorse: a horse bred for racing

horse (noun)	racehorse (noun)
solid-hoofed herbivorous quadruped domesticated since prehistoric times	a horse bred for racing
a chessman shaped to resemble the head of a horse; can move two squares horizontally and one vertically (or vice versa)
a framework for holding wood that is being sawed
a padded gymnastic apparatus on legs
troops trained to fight on horseback

horse (verb)	racehorse (verb)
provide with a horse or horses