climb up vs rise

climb up is not a noun while rise is a noun.

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

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

Other synonyms of climb up include jump.

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

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

climb up (noun)	rise (noun)
	the act of changing location in an upward direction
	increase in price or value
	the property possessed by a slope or surface that rises
	the amount a salary is increased
	an increase in cost
	a growth in strength or number or importance
	a wave that lifts the surface of the water or ground
	a movement upward; rise above the ground
	(theology) the origination of the Holy Spirit at Pentecost
	an upward slope or grade (as in a road)

climb up (verb)	rise (verb)
rise in rank or status	return from the dead
go upward with gradual or continuous progress	get up and out of bed
appear to be moving upward, as by means of tendrils	increase in value or to a higher point
	become more extreme
	go up or advance
	rise in rank or status
	exert oneself to meet a challenge
	become heartened or elated
	move upward
	increase in volume
	come to the surface
	rise to one's feet
	move to a better position in life or to a better job
	come up, of celestial bodies
	take part in a rebellion; renounce a former allegiance
	rise up
	come into existence; take on form or shape