madam vs woman

madam and woman both are nouns.

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

As nouns, woman is a hypernym of madam; that is, woman is a word with a broader meaning than madam:

Other hypernyms of madam include adult female.

madam (noun)	woman (noun)
a woman of refinement	women as a class
a woman who runs a house of prostitution	an adult female person (as opposed to a man)
	a female person who plays a significant role (wife or mistress or girlfriend) in the life of a particular man