This structural difference produces divergent verdicts when instrumental reasons are absent: negative retributivism forbids punishment while positive retributivism permits or requires it.

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Instrumental reasons(in ethics): Reasons for doing something based on whether it will help you achieve some other goal (like punishing someone to deter crime), rather than because the action itself is right or wrong.
Negative retributivism(as used in philosophy of punishment): A form of retributivism focused on limiting punishment to only what is deserved, rather than actively requiring punishment as a moral duty.
Positive retributivism(in criminal justice theory): The version of retributivism that says we are allowed to punish people who deserve it, or that we must punish them when they do.
Retributivism(as used in ethics and justice philosophy): A theory of punishment that says people deserve to be punished in proportion to the harm they caused—the worse the crime, the harsher the punishment should be.

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