wrath vs madness

wrath and madness both are nouns.

Word	Noun	Adjective	Verb	Adverb
wrath	Yes	No	No	No
madness	Yes	No	No	No

As nouns, madness is a hypernym of wrath; that is, madness is a word with a broader meaning than wrath:

Other hypernyms of wrath include fury, rage.

wrath (noun)	madness (noun)
belligerence aroused by a real or supposed wrong (personified as one of the deadly sins)	unrestrained excitement or enthusiasm
intense anger (usually on an epic scale)	the quality of being rash and foolish
	a feeling of intense anger
	obsolete terms for legal insanity
	an acute viral disease of the nervous system of warm-blooded animals (usually transmitted by the bite of a rabid animal); rabies is fatal if the virus reaches the brain