carte vs menu

carte and menu both are nouns.

Word	Noun	Adjective	Verb	Adverb
carte	Yes	No	No	No
menu	Yes	No	No	No

As nouns, carte and menu are synonyms defined as:

Other synonyms of carte include bill of fare, card, carte du jour.

carte (noun)	menu (noun)
a list of dishes available at a restaurant	an agenda of things to do
	a list of dishes available at a restaurant
	(computer science) a list of options available to a computer user
	the dishes making up a meal