umbrage vs anger

umbrage and anger both are nouns.

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

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

umbrage: a feeling of anger caused by being offended
anger: a strong emotion; a feeling that is oriented toward some real or supposed grievance

Other hypernyms of umbrage include choler, ire.

umbrage (noun)	anger (noun)
a feeling of anger caused by being offended	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

umbrage (verb)	anger (verb)
	make angry
	become angry