late 14c., revengen, "avenge oneself," from Old French revengier, revenger, variants of revenchier "take revenge, avenge" (13c., Modern French revancher), from re-, here perhaps an intensive prefix (see re-), + vengier "take revenge," from Latin vindicare "to lay claim to, avenge, punish" (see vindication). Transitive sense of "take vengeance on account of" is from early 15c. Related: Revenged; revenging; revengement.
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 Columbia Guide to Standard American English," 1993]
"retaliation for wrongs real or fancied, act of doing harm or injury in return for wrong or injury suffered," 1540s, from French revenge, a back-formation from revengier (see revenge (v.)). Hence "vindictive feeling, desire to be revenged."