madwoman vs woman

madwoman and woman both are nouns.

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

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

Other hypernyms of madwoman include lunatic, maniac, adult female.

madwoman (noun)	woman (noun)
a woman lunatic	women as a class
	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