avenge / revenge
Paying back a wrong vs. personal payback.
Avenge means to pay back a wrong in the name of justice, usually a wrong done to someone else: She avenged her brother’s death. Revenge means payback driven by personal anger or spite, and it is most often a noun: He wanted revenge. Avenging rights a wrong, and revenge settles a personal score.
Examples
Use The town vowed to avenge the fallen miners. (to see justice done for them)
Use He took revenge on the man who cheated him. (payback driven by personal anger)
Use The detective worked for years to avenge the murdered girl. (to see justice done for her)
Use She slashed his tires out of revenge. (spite, not justice)