climb vs go up

climb is a noun but go up is not a noun.

Word	Noun	Adjective	Verb	Adverb
climb	Yes	No	Yes	No
go up	No	No	Yes	No

As verbs, climb and go up are synonyms defined as:

Other synonyms of climb include rise.

As verbs, climb and go up are synonyms defined as:

Other synonyms of climb include climb up, mount.

As verbs, go up is a hypernym of climb; that is, go up is a word with a broader meaning than climb:

Other hypernyms of climb include arise, come up, lift, move up, rise, uprise.

climb (noun)	go up (noun)
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)

climb (verb)	go up (verb)
go up or advance	increase in value or to a higher point
increase in value or to a higher point	burn completely; be consumed or destroyed by fire
improve one's social status	move upward
go upward with gradual or continuous progress	go upward with gradual or continuous progress
move with effort, by grasping	be erected, built, or constructed
slope upward	move towards
	travel up