One is payed to the state, the other to another person, as in one regulates the relation to the state, the other the relation to another person.
What's your view on statutory damages for copyright infringement? "Wilful infringement" has statutory damages up to $150k per work. This is similar. Like this it's a punishment imposed by the state, through the medium of inflated damages.
No, I do not consider damages in copyright infringement a punishment. Whether damages are measured correctly or not in some case or other is beside the point I was making.
I’m confused what you define a punishment as then.