mountain peak vs peak

mountain peak and peak both are nouns.

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

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

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

mountain peak (noun)	peak (noun)
the summit of a mountain	a brim that projects to the front to shade the eyes
	the top or extreme point of something (usually a mountain or hill)
	the highest point (of something)
	the most extreme possible amount or value
	a V shape
	the highest level or degree attainable; the highest stage of development
	the period of greatest prosperity or productivity

mountain peak (verb)	peak (verb)
	to reach the highest point; attain maximum intensity, activity