madam vs adult female

madam and adult female both are nouns.

Word	Noun	Adjective	Verb	Adverb
madam	Yes	No	No	No
adult female	Yes	No	No	No

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

Other hypernyms of madam include woman.

madam (noun)	adult female (noun)
a woman of refinement	an adult female person (as opposed to a man)
a woman who runs a house of prostitution