I've never heard 'avenge angel'. Do you perhaps mean 'avenging angel'? They are quite similar - but to differentiate them, I would say: Revenge is more vengeful ;) It means to retaliate for some wrong - often even if the wrongdoer has already been punished, and is quite often excessive. Avenge is more to seek justice - either to encourage or assist with the normal justice process, or to take it's place if none is possible or likely.

Avenge is to get revenge for someone or something else, usually. If I want revenge for my father's death, I will seek to avenge him. Avenge is generally a verb, and revenge is a noun, or occasionally an adjective. I'm not sure what that expression is, but avenge angel I would take as an angel avenging someone, whereas revenge would be one getting revenge? Neither one makes a whole lot of sense to me, though.

revenge = noun avenge = verb It's that simple.