An example from my work: in Norwegian criminal law, the prosecutor can in some cases hand out what is called a «påtaleunnlatelse», which means something like «decision to not prosecute». This is a legal punishment in the sense that it goes on your criminal record, but no punishment beyond that is handed out. Basically, the prosecutor’s office can note down «we are convinced we can prove this was done, but have decided not to prosecute».
A special kind of this is the «prosessøkonomisk (process economical) påtaleunnlatelse» where in a large and complex case with many serious offences, some less serious can be non-prosecuted in this way to not spend eternity in the courtroom.
In Australian English, this is known as "Section 10".
In English English it’s a ‘caution’.
So these are kind of fun to compare. At the high level they clearly all have the same purpose: in some cases it's socially useful to have the punishment for a crime simply be a statement of "person X did this thing". But the details vary a bit:
- It seems the Australian section 10 is handed out by the court, where the English and Norwegian options dispense with a trial entirely. It also looks like a Section 10 doesn't go in a person's criminal record, unlike the other two.
- It looks like the English caution requires an admission of guilt, while the Norwegian option is at the prosecutor's discretion within the rules of applicability of the procedure. Of course someone not demanding a trial when given this can be seen as an _implicit_ admission of guilt, but the legal nuance can probably be important.
- The English and Norwegian procedures are nominally also different in who makes the decision: the English procedure is handled by the police, while in Norway it's the prosecutor's office. But this is more a theoretical than practical difference I think, because the Norwegian prosecutor's office is organized differently than the English Crown Prosecution Service: here, the lowest levels of prosecutors are integrated into the police services they work with, so in practice I think it works out much the same.
In law of England and Wales we also have recording of non-crimes, which aren't cautions (it goes back to combating institutional racism).