postilion vs horseback rider

postilion and horseback rider both are nouns.

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

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

postilion: someone who rides the near horse of a pair in order to guide the horses pulling a carriage (especially a carriage without a coachman)
horseback rider: a person skilled in equitation

Other hypernyms of postilion include equestrian.

postilion (noun)	horseback rider (noun)
someone who rides the near horse of a pair in order to guide the horses pulling a carriage (especially a carriage without a coachman)	a person skilled in equitation