ascent vs climbing

ascent and climbing both are nouns.

Word	Noun	Adjective	Verb	Adverb
ascent	Yes	No	No	No
climbing	Yes	No	No	No

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

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

ascent (noun)	climbing (noun)
the act of changing location in an upward direction	an event that involves rising to a higher point (as in altitude or temperature or intensity etc.)
a movement upward; rise above the ground
an upward slope or grade (as in a road)