ill temper vs anger

ill temper and anger both are nouns.

Word	Noun	Adjective	Verb	Adverb
ill temper	Yes	No	No	No
anger	Yes	No	Yes	No

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

ill temper: a persisting angry mood
anger: a strong emotion; a feeling that is oriented toward some real or supposed grievance

Other hypernyms of ill temper include choler, ire.

ill temper (noun)	anger (noun)
a persisting angry mood	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
	the state of being angry

ill temper (verb)	anger (verb)
	make angry
	become angry