When you try to get vengeance for people who’ve been wronged, you want to avenge them. You can also avenge a wrong itself: “He avenged the murder by taking vengeance on the killer.” Substituting “revenge” for “avenge” in such contexts is very common, but frowned on by some people. They feel that if you seek revenge in the pursuit of justice you want to avenge wrongs: not revenge them.
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