riding vs equitation

riding and equitation both are nouns.

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

As nouns, riding and equitation are synonyms defined as:

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

Other synonyms of riding include horseback riding.

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