Punishment inflicted or retribution exacted for an injury or wrong.
Vengeance is a legal action taken by a legal entity, i.e. a government or ruler. It is the infliction of a penalty as an act of legal judgement; the carrying out of a sentence against a convicted person or people by a legal authority.
God used this word 45 times in Scripture; 39 times to Israel in the Old Testament, once about Paul in the book of Acts, 3 times to the Body of Christ, and 2 times to Israel in the tribulation … He said what He meant, and He meant what he said.
See also Judgement, Justice, Revenge