mountain peak vs crest

mountain peak and crest both are nouns.

Word	Noun	Adjective	Verb	Adverb
mountain peak	Yes	No	No	No
crest	Yes	No	Yes	No

As nouns, crest is a hypernym of mountain peak; that is, crest is a word with a broader meaning than mountain peak:

Other hypernyms of mountain peak include crown, peak, summit, tip, top.

mountain peak (noun)	crest (noun)
the summit of a mountain	a showy growth of e.g. feathers or skin on the head of a bird or other animal
	(heraldry) in medieval times, an emblem used to decorate a helmet
	the center of a cambered road
	the top line of a hill, mountain, or wave
	the top or extreme point of something (usually a mountain or hill)

mountain peak (verb)	crest (verb)
	reach a high point
	lie at the top of