Being offended means someone else has done something, and you don't like it, and you feel it's up to them to change whatever it is, not you.
Being angry means that something has happened, and you feel it personally enough to want to get off your arse and take action to change things.
People who are offended talk forever, but don't do sh*t, so nothing changes.
People who are angry may do something wrong, or may do something stupid, but at least they're doing something.,
Not a 100% rule (there is not a thing I can do about the light turning red JUST when I get to the intersection), but it's a useful distinction. I can ignore 'offended' people all damn day long!