rock climber vs climber

rock climber and climber both are nouns.

Word	Noun	Adjective	Verb	Adverb
rock climber	Yes	No	No	No
climber	Yes	No	No	No

As nouns, climber is a hypernym of rock climber; that is, climber is a word with a broader meaning than rock climber:

rock climber: a climber of vertical rock faces
climber: someone who climbs as a sport; especially someone who climbs mountains

rock climber (noun)	climber (noun)
a climber of vertical rock faces	an iron spike attached to the shoe to prevent slipping on ice when walking or climbing
	someone who climbs as a sport; especially someone who climbs mountains
	someone seeking social prominence by obsequious behavior
	someone who ascends on foot
	a vine or climbing plant that readily grows up a support or over other plants