rage vs wrath

rage and wrath both are nouns.

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

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

Other hyponyms of rage include lividity.

rage (noun)	wrath (noun)
an interest followed with exaggerated zeal	belligerence aroused by a real or supposed wrong (personified as one of the deadly sins)
a feeling of intense anger	intense anger (usually on an epic scale)
a state of extreme anger
violent state of the elements
something that is desired intensely

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