In Marxist analysis, there is a distinction drawn between personal property and private property. The former is one's possessions. The latter is exclusionary ownership over economically active assets, i.e. the means of production. For example, land, factories, machinery. The way private ownership works under capitalism is tangibly different from ownership forms anterior to it, for example feudal titles to land. In many societies, including say England before the industrial revolution, the primary means of production was the land itself which wasn't owned by anyone: It was the commons that commoners are named after. It was enclosure, a generations-long political and violent process which converted the common land into private property. This had two implications:

1) There was now a class of people that owned most of the resources necessary for a human to survive by their own work.

2) There was now a massive class of landless people who could no longer sustain themselves through their own work of the commons that now needed jobs.

This is the sort of system of property that is strongly associated with capitalism that need not exist in other cultures.