fury vs anger

fury and anger both are nouns.

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

As nouns, anger is a hypernym of fury; that is, anger is a word with a broader meaning than fury:

fury: a feeling of intense anger
anger: a strong emotion; a feeling that is oriented toward some real or supposed grievance

Other hypernyms of fury include choler, ire.

fury (noun)	anger (noun)
the property of being wild or turbulent	belligerence aroused by a real or supposed wrong (personified as one of the deadly sins)
a feeling of intense anger	a strong emotion; a feeling that is oriented toward some real or supposed grievance
state of violent mental agitation	the state of being angry

fury (verb)	anger (verb)
	make angry
	become angry