horseback riding vs equitation

horseback riding and equitation both are nouns.

Word	Noun	Adjective	Verb	Adverb
horseback riding	Yes	No	No	No
equitation	Yes	No	No	No

As nouns, horseback riding and equitation are synonyms defined as:

horseback riding and equitation: the sport of sitting on the back of a horse while controlling its movements

Other synonyms of horseback riding include riding.

horseback riding (noun)	equitation (noun)
travel by being carried on horseback	the sport of sitting on the back of a horse while controlling its movements
the sport of sitting on the back of a horse while controlling its movements