anger vs offend

anger is a noun but offend is not a noun.

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

As verbs, offend is a hyponym of anger; that is, offend is a word with a more specific, narrower meaning than anger:

anger (noun)	offend (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

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