formal vs cotilion

formal and cotilion both are nouns.

Word	Noun	Adjective	Verb	Adverb
formal	Yes	Yes	No	No
cotilion	Yes	No	No	No

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

Other hyponyms of formal include cotillion, fancy-dress ball, masked ball, masquerade ball, prom, promenade.

formal (noun)	cotilion (noun)
a gown for evening wear	a lively dance originating in France in the 18th century
a lavish dance requiring formal attire	a ball at which young ladies are presented to society

formal (adjective)	cotilion (adjective)
being in accord with established forms and conventions and requirements (as e.g. of formal dress)
(of spoken and written language) adhering to traditional standards of correctness and without casual, contracted, and colloquial forms
refined or imposing in manner or appearance; befitting a royal court
logically deductive
represented in simplified or symbolic form
characteristic of or befitting a person in authority