Marx is clear about this, BTW. The distinction between private property (i.e. capital) and personal property, is that personal property is owned for its use value (you own a trenchcoat to protect yourself from the cold, or you own a house to live in it), whereas private property is owned for its monetary revalorization capability (you own a trenchcoat to rent it in a costumes store, you own a house to rent it to someone else). The same object can be used for its use value, and then it's it's personal property; or it can be used in the capital revalorization cycle, and then it's private property.