[Anglika]

Revenge can be either a noun or a verb:

• noun 1 retaliation for an injury or wrong. 2 the desire to inflict such retaliation.
• verb 1 (revenge oneself or be revenged) inflict revenge for an injury or wrong done to oneself. 2 inflict revenge on behalf of (someone else) or for (a wrong or injury)
— ORIGIN Old French revencher, from Latin vindicare ‘claim, avenge

Avenge is only a verb

• verb inflict harm in return for (a wrong). — DERIVATIVES avenger noun.
— ORIGIN Old French avengier, from Latin vindicare ‘vindicate
Both mean “getting even, punishing someone for having injured you or yours” .

To avenge is “to get revenge” or “to take vengeance”; it suggests the administration of just punishment for a criminal or immoral act.

Revenge seems to stress the idea of retaliation a bit more strongly and implies real hatred as its motivation. The verb revenge is usually used with a reflexive pronoun: He revenged himself on those who had killed his parents;