In leftist theory, there is a difference between "private property" and "personal property/belongings."

Private property is property owned specifically for generating profit. For example, owning a home to rent it out, or shares in a company.

Personal property/belongings are things you use. For example, the home you live in, your car, your toothbrush, etc. Under socialism, if multiple people use something, then you all partly own it, e.g. you would also partly own the business you work for ("the means of production"). You own everything you use and nothing you don't