climb vs come on

climb is a noun but come on is not a noun.

Word	Noun	Adjective	Verb	Adverb
climb	Yes	No	Yes	No
come on	No	No	Yes	No

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

Other hypernyms of climb include advance, come along, get along, get on, progress, shape up.

climb (noun)	come on (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)	come on (verb)
go up or advance	occur or become available
increase in value or to a higher point	appear or become visible; make a showing
improve one's social status	develop in a positive way
go upward with gradual or continuous progress	start running, functioning, or operating
move with effort, by grasping	move towards
slope upward