It has a difference because if your goal is deterrence, then if it can be shown that other means of deterrence are better, then it is logical to apply those even if they reduce the apparent punishment, while if your goal is punishment you might want to keep punishing people even if it is shown to not be effective.
See e.g. the debates over lenient prisons in Scandinavia such as Bastøy Prison, where the lenient treatment is seen as justified on a deterrence and recidivism basis but which would be seen as negative if you see the goal of the sentencing to be harsh in order to punish.
See e.g. the debates over lenient prisons in Scandinavia such as Bastøy Prison, where the lenient treatment is seen as justified on a deterrence and recidivism basis but which would be seen as negative if you see the goal of the sentencing to be harsh in order to punish.