competence vs ability

competence and ability both are nouns.

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

As nouns, ability is a hypernym of competence; that is, ability is a word with a broader meaning than competence:

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

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