anger vs rage

anger and rage both are nouns.

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

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

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

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

anger (noun)	rage (noun)
belligerence aroused by a real or supposed wrong (personified as one of the deadly sins)	an interest followed with exaggerated zeal
a strong emotion; a feeling that is oriented toward some real or supposed grievance	a feeling of intense anger
the state of being angry	a state of extreme anger
	violent state of the elements
	something that is desired intensely

anger (verb)	rage (verb)
make angry	feel intense anger
become angry	be violent; as of fires and storms
	behave violently, as if in state of a great anger