horseback rider vs rider

horseback rider and rider both are nouns.

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

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

horseback rider (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)