fancy-dress ball vs formal

fancy-dress ball and formal both are nouns.

Word	Noun	Adjective	Verb	Adverb
fancy-dress ball	Yes	No	No	No
formal	Yes	Yes	No	No

As nouns, formal is a hypernym of fancy-dress ball; that is, formal is a word with a broader meaning than fancy-dress ball:

Other hypernyms of fancy-dress ball include ball, mask, masque, masquerade, masquerade party.

fancy-dress ball (noun)	formal (noun)
a ball at which guests wear costumes and masks	a gown for evening wear
	a lavish dance requiring formal attire

fancy-dress ball (adjective)	formal (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