postillion vs horseback rider

postillion and horseback rider both are nouns.

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

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

postillion: 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 postillion include equestrian.

postillion (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