pony vs race horse

pony and race horse both are nouns.

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

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

Other hypernyms of pony include bangtail, racehorse.

pony (noun)	race horse (noun)
any of various breeds of small gentle horses usually less than five feet high at the shoulder	a horse bred for racing
a range horse of the western United States
an informal term for a racehorse
a small glass adequate to hold a single swallow of whiskey
a literal translation used in studying a foreign language (often used illicitly)