ability vs competence

ability and competence both are nouns.

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

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

ability: the quality of being able to perform; a quality that permits or facilitates achievement or accomplishment
competence: the quality of being adequately or well qualified physically and intellectually

ability (noun)	competence (noun)
the quality of being able to perform; a quality that permits or facilitates achievement or accomplishment	the quality of being adequately or well qualified physically and intellectually
possession of the qualities (especially mental qualities) required to do something or get something done