aesthete vs connoisseur

aesthete and connoisseur both are nouns.

Word	Noun	Adjective	Verb	Adverb
aesthete	Yes	No	No	No
connoisseur	Yes	No	No	No

As nouns, connoisseur is a hypernym of aesthete; that is, connoisseur is a word with a broader meaning than aesthete:

aesthete: one who professes great sensitivity to the beauty of art and nature
connoisseur: an expert able to appreciate a field; especially in the fine arts

Other hypernyms of aesthete include cognoscente.

aesthete (noun)	connoisseur (noun)
one who professes great sensitivity to the beauty of art and nature	an expert able to appreciate a field; especially in the fine arts