equitation vs horseback riding

equitation and horseback riding both are nouns.

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

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

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

Other synonyms of equitation include riding.

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