anger vs wrath

anger and wrath both are nouns.

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

As nouns, anger and wrath are synonyms defined as:

anger and wrath: belligerence aroused by a real or supposed wrong (personified as one of the deadly sins)

Other synonyms of anger include ira, ire.

anger (noun)	wrath (noun)
belligerence aroused by a real or supposed wrong (personified as one of the deadly sins)	belligerence aroused by a real or supposed wrong (personified as one of the deadly sins)
a strong emotion; a feeling that is oriented toward some real or supposed grievance	intense anger (usually on an epic scale)
the state of being angry

anger (verb)	wrath (verb)
make angry
become angry