maniac vs madman

maniac and madman both are nouns.

Word	Noun	Adjective	Verb	Adverb
maniac	Yes	Yes	No	No
madman	Yes	No	No	No

As nouns, madman is a hyponym of maniac; that is, madman is a word with a more specific, narrower meaning than maniac:

Other hyponyms of maniac include crazy, looney, loony, nutcase, weirdo, bedlamite, pyromaniac, madwoman.

maniac (noun)	madman (noun)
an insane person	a male insane person
a person who has an obsession with or excessive enthusiasm for something

maniac (adjective)	madman (adjective)
wildly disordered