I am trying to understand the distinction made specifically by Pierre-Joseph Proudhon in his work, What is Property?
I've never read the book you are referring to but it sounds like he is making the distinction with what would today be called private and personal property; the former is larger properties-land, houses, means of production, etc- while the latter is personal commodities- books, toothbrushes, cell phones, etc. It sounds like "possessive property" is just another word for personal property. Unless he actually makes a large distinction in his book/theory, I would say this is his intent: to highlight this difference between the smaller use-values you own and the means of production and land owned by the bourgeoisie.