offend vs anger

offend is not a noun while anger is a noun.

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

As verbs, anger is a hypernym of offend; that is, anger is a word with a broader meaning than offend:

offend (noun)	anger (noun)
	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

offend (verb)	anger (verb)
hurt the feelings of	make angry
cause to feel resentment or indignation	become angry
strike with disgust or revulsion
act in disregard of laws, rules, contracts, or promises