climb down vs come down

climb down and come down both are verbs.

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

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

Other hypernyms of climb down include descend, fall, go down.

climb down (verb)	come down (verb)
come down	get sick
	be the essential element
	criticize or reprimand harshly
	move downward and lower, but not necessarily all the way
	fall from clouds