rise vs climb

rise and climb both are nouns.

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

As nouns, climb is a hyponym of rise; that is, climb is a word with a more specific, narrower meaning than rise:

Other hyponyms of rise include levitation, heave, heaving, mount, soar, zoom.

As nouns, climb is a hyponym of rise; that is, climb is a word with a more specific, narrower meaning than rise:

rise: a movement upward; rise above the ground
climb: an event that involves rising to a higher point (as in altitude or temperature or intensity etc.)

As nouns, rise and climb are synonyms defined as:

Other synonyms of rise include acclivity, ascent, raise, upgrade.

As verbs, rise and climb are synonyms defined as:

Other synonyms of rise include go up.

As verbs, rise and climb are synonyms defined as:

Other synonyms of rise include mount, wax.

As verbs, climb is a hyponym of rise; that is, climb is a word with a more specific, narrower meaning than rise:

rise (noun)	climb (noun)
the act of changing location in an upward direction	the act of climbing something
increase in price or value	an event that involves rising to a higher point (as in altitude or temperature or intensity etc.)
the property possessed by a slope or surface that rises	an upward slope or grade (as in a road)
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)

rise (verb)	climb (verb)
return from the dead	go up or advance
get up and out of bed	increase in value or to a higher point
increase in value or to a higher point	improve one's social status
become more extreme	go upward with gradual or continuous progress
go up or advance	move with effort, by grasping
rise in rank or status	slope upward
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