Restitutive and vengeful punishment are distinct aims that people conflate

Evidence

Vengeance is another justification for executing murderers. People often confuse restitutive punishment with vengeful punishment. Restitution is aimed at restoring justice, but with restitution, excessively harsh punishment is disavowed. In contrast, vengeful punishment—the harsher the better—is aimed at inflicting suffering on offenders. — Albert Bandura, Moral Disengagement, 1893

Categorization

• corroborated: 3 independent passages support this claim — Albert Bandura, Moral Disengagement: How People Do Harm…, 1893