madam vs lady

madam and lady both are nouns.

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

As nouns, madam and lady are synonyms defined as:

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

madam (noun)	lady (noun)
a woman of refinement	a woman of refinement
a woman who runs a house of prostitution	a polite name for any woman