anger vs emotion

anger and emotion both are nouns.

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

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

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

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

anger (verb)	emotion (verb)
make angry
become angry