madam vs gentlewoman

madam and gentlewoman both are nouns.

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

As nouns, madam and gentlewoman are synonyms defined as:

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

madam (noun)	gentlewoman (noun)
a woman of refinement	a woman of refinement
a woman who runs a house of prostitution