madness vs fury

madness and fury both are nouns.

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

As nouns, madness and fury are synonyms defined as:

Other synonyms of madness include rage.

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