Vengeance vs. Avenge: What's the Difference?

Vengeance and Avenge Definitions
Vengeance
Infliction of punishment in return for a wrong committed; retribution.
Avenge
To inflict a punishment or penalty in return for; revenge
Avenge a murder.
Vengeance
Revenge taken for an insult, injury, or other wrong.
Avenge
To take vengeance on behalf of
Avenged their wronged parents.
Vengeance
Desire for revenge.
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Avenge
(transitive) To take vengeance (for); to exact satisfaction for by punishing the injuring party; to vindicate by inflicting pain or evil on a wrongdoer.
To avenge the murder of his brother
Vengeance
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.
To execute fierce vengeance on his foes.
Avenge
(reflexive) To revenge oneself (on or upon someone).
Vengeance
Harm; mischief.
Avenge
To take vengeance.
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Vengeance
The act of taking revenge (harming someone in retaliation for something harmful that they have done) especially in the next life;
Vengeance is mine; I will repay, saith the Lord
For vengeance I would do nothing. This nation is too great to look for mere revenge
He swore vengeance on the man who betrayed him
The swiftness of divine retribution
Avenge
To treat revengefully; to wreak vengeance on.
Avenge
(archaic) An act of vengeance; a revenge.
Avenge
To take vengeance for; to exact satisfaction for by punishing the injuring party; to vindicate by inflicting pain or evil on a wrongdoer.
He will avenge the blood of his servants.
Avenge, O Lord, thy slaughtered saints, whose bonesLie scattered on the Alpine mountains cold.
He had avenged himself on them by havoc such as England had never before seen.
Avenge
To treat revengefully; to wreak vengeance on.
Thy judgment in avenging thine enemies.
I avenge myself upon another, or I avenge another, or I avenge a wrong. I revenge only myself, and that upon another.
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Avenge
To take vengeance.
Avenge
Vengeance; revenge.
Avenge
Take revenge for a perceived wrong;
He wants to avenge the murder of his brother