madam vs ma'am

madam and ma'am both are nouns.

Word	Noun	Adjective	Verb	Adverb
madam	Yes	No	No	No
ma'am	Yes	No	No	No

As nouns, madam and ma'am are synonyms defined as:

Other synonyms of madam include dame, gentlewoman, lady.

madam (noun)	ma'am (noun)
a woman of refinement	a woman of refinement
a woman who runs a house of prostitution