The distinction between personal and private property has nothing to do with the state. The same distinction is made by socialist anarchists. What makes property private rather than personal is that your use of the property affects other people. Like if you claim as your private property the right to fish a fishery, that's not the same as a personal possession, because your use of that property can affect other people's lives and the health of species and ecosystems. People should be allowed to have personal property but they can't have private property because in order to have actual democracy we have to have control over decisions about resources that affect our lives.
The distinction between personal and private property has nothing to do with the state. The same distinction is made by socialist anarchists. What makes property private rather than personal is that your use of the property affects other people. Like if you claim as your private property the right to fish a fishery, that's not the same as a personal possession, because your use of that property can affect other people's lives and the health of species and ecosystems. People should be allowed to have personal property but they can't have private property because in order to have actual democracy we have to have control over decisions about resources that affect our lives.