climber vs rock climber

climber and rock climber both are nouns.

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

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

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

Other hyponyms of climber include escalader, mountain climber, mountaineer, cragsman.

climber (noun)	rock climber (noun)
an iron spike attached to the shoe to prevent slipping on ice when walking or climbing	a climber of vertical rock faces
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