ability vs skill

ability and skill both are nouns.

Word	Noun	Adjective	Verb	Adverb
ability	Yes	No	No	No
skill	Yes	No	No	No

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

ability: possession of the qualities (especially mental qualities) required to do something or get something done
skill: ability to produce solutions in some problem domain

ability (noun)	skill (noun)
the quality of being able to perform; a quality that permits or facilitates achievement or accomplishment	ability to produce solutions in some problem domain
possession of the qualities (especially mental qualities) required to do something or get something done	an ability that has been acquired by training