It may have become that, but was it always that way, though?
I grew up being pretty clear on the distinction between purchasing a book in a bookshop and borrowing a book from the school or public library.
Does that mean that you don’t own the book?
Ownership is not so clear cut.
You still get value from reading the book. You get no value from a pogo-free pogo stick
Very good point that proves "ownership" means different things: private property under capitalism is different from a common/public property such as a book from a library. For most of history, land was not "owned" by anyone. See also "enclosure of the commons" for some reading on the topic.
Use-based "ownership" (personal belongings) is not "private property" (a religious belief that prevents people from using a resource that could benefit them such as empty dwellings), and is not "collective property" (shared resource managed by a community), and is not "public domain" (shared abundant resources such as air or water in some regions). All of these approaches can be considered forms of ownership/property, but they vary wildly in principles and applications.
There is no practical difference between personal property and private property. If i have lathe in my workshop that i use just for hobby purposes, then it is personal property. If i started business, put that lathe in that business and use it for work, then it is private property / capital. But in both cases it is the same lathe that someone has to produce, someone has to pay for it, someone has to maintain it and can be bought and sold on open market.