rider vs equestrian

rider and equestrian both are nouns.

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

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

Other hyponyms of rider include horseback rider.

rider (noun)	equestrian (noun)
a clause that is appended to a legislative bill	a person skilled in equitation
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)

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