How is private property any different than the state in a certain way?

Hello! I am personally somebody very sympathetic to the NAP. I think it is a great concept and ground for ethics. I am not someone who is fundamentally anti-libertarian. In fact I am very sympathetic to libertarianism.

I just want to understand this: How is private property any different than state owned? For example if I were to allocate a country zize amount of land in ancapistan (through voluntary exchange) and then a bunch of people from the entire world had to flee from their homes because they got nuked or something and they had to come to me and I invited them in and forced them to follow my own personal laws and dress codes on my private property and taxation and so on then how would that be different from the state?

Or what if 200 individuals owned the entire worlds surface area and had divided it up differently based on who owned what private property. And everyone on their private property enforced their own laws and so on. How would that be different from the states today?

Of course an objection to this is that in practice this would never happen due to how markets behave and how people behave and so on but in theory this state of affairs would be allowed under the non-aggression principle right? Like, why would it not be allowed?