People tend to misuse philosophical and legal terms pretty often, like free speech being used as a shield from criticism or ‘it’s a free country’ when talking about trespassing, etc. Private property in communist terms refers to public goods (land, rivers, bodies of water, geological formations, animal habitats, etc.) which have been enclosed by private interests such that individuals no longer have access to the natural resources of the land unless they sell their labor. We call people who enclose the Commons the bourgeoise. You can learn more about this in Proudhon’s What is Property?.

A good example of this is the Manifest Destiny of North America, as it happened very recently and involves millions of government records going back to the 16th century. Native Americans had fairly advanced societies that managed to operate while preserving the Commons. Mississippian culture and its adjacent relatives covered nearly half of what we now call the US, and they managed the land quite heavily with fire-managed hunting grounds, oak savannas, maize farms, fisheries, earthworks, and a large network of roads and canoe routes. All of these things were held in common, meaning entire tribes were expected to manage the upkeep of these resources as a collective and as long as no one took too much conflict was negligible.

When the United States was established, they immediately declared war on Native Americans, surveyed the land and divided it into subdivisions for private sale according to the Public Land Survey System. Under this system the distribution of wealth among settlers was psuedo-random (ie. occasionally impoverished farmers profited from oil/mineral rights but usually got driven off by bigger fish), but with a weight toward the wealthy class who could accumulate entire regions through speculation or preying on people who defaulted on their loans. We can also see this in modern Iraq with the expropriation of oil fields by western companies (with the income, wages, and profits being funneled out of the country by western contractors), when the land was previously managed directly by the Iraqi government with profits going toward public infrastructure and administration.

Basically, the phrase we normally use is “we’re not coming after your toothbrush”. Soviet citizens didn’t own their homes, but they had a legal right to a home for basically free, and the state painstakingly ensured that construction of housing kept up with population growth. Similarly, in Vietnam after the war, all citizens were guaranteed a plot of land from the state that was theirs to use for as long as they lived. To this day China and Vietnam have extremely high home ownership rates and low rates of homelessness. And not only did Russians own cars but even many North Koreans now own cars. Socialism isn’t meant to make people destitute or into hippie colonies who all share one bed. It’s about preventing people who hoard from parasitizing the rest of society for their own bloated sense of self-worth.