lunatic vs madman

lunatic and madman both are nouns.

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

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

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

lunatic (noun)	madman (noun)
an insane person	a male insane person
a reckless impetuous irresponsible person

lunatic (adjective)	madman (adjective)
insane and believed to be affected by the phases of the moon