madam vs dame

madam and dame both are nouns.

Word	Noun	Adjective	Verb	Adverb
madam	Yes	No	No	No
dame	Yes	No	No	No

As nouns, madam and dame are synonyms defined as:

Other synonyms of madam include gentlewoman, lady, ma'am.

madam (noun)	dame (noun)
a woman of refinement	informal terms for a (young) woman
a woman who runs a house of prostitution	a woman of refinement