mountain climbing vs climb

mountain climbing and climb both are nouns.

Word	Noun	Adjective	Verb	Adverb
mountain climbing	Yes	No	No	No
climb	Yes	No	Yes	No

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

Other hypernyms of mountain climbing include mount.

mountain climbing (noun)	climb (noun)
the activity of climbing a mountain	the act of climbing something
	an event that involves rising to a higher point (as in altitude or temperature or intensity etc.)
	an upward slope or grade (as in a road)

mountain climbing (verb)	climb (verb)
	go up or advance
	increase in value or to a higher point
	improve one's social status
	go upward with gradual or continuous progress
	move with effort, by grasping
	slope upward