Vengeance, n.
Etymology: [F. vengeance, fr. venger to avenge, L. vindicare to lay claim to, defend, avenge, fr. vindex a claimant, defender, avenger, the first part of which is of uncertain origin, and the last part akin to dicere to say. See Diction, and cf. Avenge, Revenge, Vindicate.]
1. Punishment inflicted in return for an injury or an offense; retribution; -- often, in a bad sense, passionate or unrestrained revenge. To me belongeth vengeance and recompense. Deut. xxxii. 35. To execute fierce vengeance on his foes. Milton.
2. Harm; mischief. [Obs.] Shak. What a vengeance, or What the vengeance, what! -- emphatically. [Obs.] "But what a vengeance makes thee fly!" Hudibras. "What the vengeance! Could he not speak 'em fair" Shak. -- With a vengeance, with great violence; as, to strike with a vengeance. [Colloq.]
Shades of meaning
Fernald has no entry of its own for vengeance; he lists it under revenge.
Where he writes about it:
Vengeance, which once meant an indignant vindication of justice, now signifies the most furious and unsparing revenge. — from revenge
Revenge emphasizes more the personal injury in return for which it is inflicted, vengeance the ill desert of those upon whom it is inflicted. — from revenge