bill of fare vs carte

bill of fare and carte both are nouns.

Word	Noun	Adjective	Verb	Adverb
bill of fare	Yes	No	No	No
carte	Yes	No	No	No

As nouns, bill of fare and carte are synonyms defined as:

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

bill of fare (noun)	carte (noun)
a list of dishes available at a restaurant	a list of dishes available at a restaurant