equestrian vs rider

equestrian and rider both are nouns.

Word	Noun	Adjective	Verb	Adverb
equestrian	Yes	Yes	No	No
rider	Yes	No	No	No

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

equestrian (noun)	rider (noun)
a person skilled in equitation	a clause that is appended to a legislative bill
	a traveler who actively rides an animal (as a horse or camel)
	a traveler riding in a vehicle (a boat or bus or car or plane or train etc) who is not operating it
	a traveler who actively rides a vehicle (as a bicycle or motorcycle)

equestrian (adjective)	rider (adjective)
of or relating to or featuring horseback riding
of or relating to or composed of knights