menu vs carte

menu and carte both are nouns.

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

As nouns, menu and carte are synonyms defined as:

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

menu (noun)	carte (noun)
an agenda of things to do	a list of dishes available at a restaurant
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