equestrian sport vs equitation

equestrian sport and equitation both are nouns.

Word	Noun	Adjective	Verb	Adverb
equestrian sport	Yes	No	No	No
equitation	Yes	No	No	No

As nouns, equitation is a hypernym of equestrian sport; that is, equitation is a word with a broader meaning than equestrian sport:

equestrian sport: a sport that tests horsemanship
equitation: the sport of sitting on the back of a horse while controlling its movements

Other hypernyms of equestrian sport include horseback riding, riding.

equestrian sport (noun)	equitation (noun)
a sport that tests horsemanship	the sport of sitting on the back of a horse while controlling its movements