Compensation for a criminal offense

Is it indeed a fine in the two cases I mentioned (and also in double payments)?
Is there anything else from Torah law that is a fine that arises from what can be defined today as a criminal offense and not a tortious act, and is paid to the victim of the offense?
I saw that regarding conspiring witnesses there is a dispute as to whether the payment imposed on them is from monetary law or from fine law. (Wikipedia). And I saw that there are fines that are completely related to tort law.
I assume I made a mistake here. If you could clarify a bit..

In Halacha, there are two types of payments (there are more, such as ransom, but this is what is important for our purposes): money and a fine. Money is compensation for damage or repayment of a loan, etc. Naturally, in money payments, the amount of the payment is the principal (what I lent or what I borrowed). Any payment that is not money, and the indication is that it is fixed (not dependent on the reason for the payment, except for half the damage in money damages) and its value is different from the principal, is a fine (except for half the damage in bundles). For example, money damages require payment of half the damage, which is a fine. Theft requires double the amount, which is a fine. Rape and seduction also require payment of a fine (and compensation).
Any payment of a fine is a punitive payment. The penalty can sometimes be for a side issue. For example, in a financial apostasy under oath, one pays a fifth, which is probably a penalty for the oath (because in a financial apostasy without an oath, one does not pay this).
Regarding fines that involve torts, I am not sure I understood the question. There are several fines that are paid for harming another: half the damage for damage to property, double for theft, fifty shillings for rape, and so on.
Regarding conspiring witnesses, there is indeed a disagreement about whether it is a fine or a fine. The commentators discussed this because there is a situation where no damage was caused, but only that they wanted it to be caused. Therefore, it should be a fine. It seems to me that the Torah sees this as if they actually caused it, and therefore some define it as a fine. But this is an exceptional case.

Thank you very much.