ability vs cognition

ability and cognition both are nouns.

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

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

ability: possession of the qualities (especially mental qualities) required to do something or get something done
cognition: the psychological result of perception and learning and reasoning

Other hypernyms of ability include knowledge, noesis.

ability (noun)	cognition (noun)
the quality of being able to perform; a quality that permits or facilitates achievement or accomplishment	the psychological result of perception and learning and reasoning
possession of the qualities (especially mental qualities) required to do something or get something done