fury vs madness

fury and madness both are nouns.

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

As nouns, fury and madness are synonyms defined as:

Other synonyms of fury include rage.

fury (noun)	madness (noun)
the property of being wild or turbulent	unrestrained excitement or enthusiasm
a feeling of intense anger	the quality of being rash and foolish
state of violent mental agitation	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