anonymous question

This is roughly like asking what the difference is between equality and a jury trial. The first is a principle. The second is an institution. Between them is a cause-and-effect relationship.

NAP is the non-aggression principle, stating that no one has the right to use aggressive violence with impunity. Contractual jurisdictions are an institution for conflict resolution based on adherence to the NAP.

The point of contractual jurisdictions is that one subject enters into an agreement with another subject stating that they are subject to their jurisdiction. The agreement also specifies what limitations this jurisdiction has.
The existence of a contract between the court and the subject is a mandatory condition that ensures compliance with the NAP, since under the contract, the subject agrees to execute the court’s decision or agrees that they will be forced to execute it. Without such prior consent, an attempt to force a convicted person to execute a court decision becomes a violation of the non-aggression principle.

The most elementary example of a contractual jurisdiction is an arbitration court. Two parties to a conflict enter into a contract with a court to resolve one specific conflict, pledging to execute the court’s decision regardless of what it may be. An arbitration court provides the highest possible degree of fairness in conflict resolution, but is poorly suited for cases of extreme bitterness between parties, as well as situations where the parties are barely acquainted and simply cannot find a single person whom both parties trust.

In cases where a pure arbitration court is difficult, intermediaries begin to step in. I entrust the settlement of my conflict to someone I have chosen as my representative, and after some effort, they provide me with a result: here the opponent is ready to make such-and-such a concession, here it makes sense for me to make a concession, I can also count on such-and-such compensation, but I must pay such-and-such for the mediation. I agree to this, and a settlement occurs. Or I disagree and negotiations continue.

The more stable a society is, the more likely it is that such mediation contracts will become more long-term and the results of their activity more predictable. People generally love to generalize and average things out to save effort and not worry about minor details.
Thus arises what is usually meant by the words “contractual jurisdictions,” although this is only a specific case of them: a system in which practically everyone is bound by a permanent contract with one jurisdiction or another, and it is that jurisdiction that handles all their conflicts, whether they bring claims against others or others bring claims against them. A contractual jurisdiction can be freely changed, but this will likely happen no more often than people change mobile operators today.

To a certain approximation, such a judicial system existed in Iceland during the Age of Sagas, that is, in the period of the absence of a state, when jurisdiction, along with priestly functions, was carried out by the so-called godi, and a landowner could enter one godord or another or move to a different one.

For the geeks, I can even provide a link with a description of this legal system.