athletics vs equitation

athletics and equitation both are nouns.

Word	Noun	Adjective	Verb	Adverb
athletics	Yes	No	No	No
equitation	Yes	No	No	No

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

athletics: an active diversion requiring physical exertion and competition
equitation: the sport of sitting on the back of a horse while controlling its movements

athletics (noun)	equitation (noun)
an active diversion requiring physical exertion and competition	the sport of sitting on the back of a horse while controlling its movements
participation in sports events as an extracurricular activity
a contest between athletes