What is the line between justice and revenge called? Or better put, when does justice become an act of revenge?

Retributivists about punishment are keen to distinguish between retributive justice and revenge. They presumably distinguish between punishment as restribution -- where that involves inflicting punishment for wrongdoing because it is wrong and in proportion to is wrongness -- from punishment as revenge -- where that involves punishing indpendently of wrongfulness or out of proportion to wrongfulness. Still, even if a private citizen exacts proportional retribution that smacks of revenge, doesn't it? If so, revenge may sometimes involve a wrongful assumption of penal authority.