If you own something, you can (legally) sell it. It may be here, it may be somewhere else. You may or may not have use of it at the moment if you're loaned it or rented it to someone else, but it legally belongs to you and you hold power over it.
If you possess something, you can use it. It is probably in your hands or on your person, though it also applies to things like skills and knowledge (since you can use them, but you can't sell them). There are times that we'll talk about possession for things that aren't so close at hand-like the house I possess but do not own.
I am renting my house. I possess the house and am able to make use of it as I wish, but I cannot sell it as I am not the legal owner. My landlord owns the house, but he does not possess it. He's not allowed to come in and sleep here, but he could sell the house to someone else. There are some things that people commonly possess without owning (cars, if they've leased them. Houses, if they're rented. Passports and certain official documents, which are legally owned by the government or issuer but used and possessed by the person they are issued for), and some things that are commonly owned without being possessed (intellectual property, for example).
However, usually, possession implies ownership and ownership implies at least potential possession, so the difference between the two often doesn't matter and they are sometimes used interchangeably. If we're looking to move something and I ask if you own a truck, I don't really care if you properly own the truck or lease it or whatever-I care whether you can bring a truck to help move the stuff. In my experience, "own" tends to be more commonly used, or "have" can be used (somewhat informally) in situations where both are acceptable.
If you're looking for a rule, consider what what's being emphasized. Legal ownership? Use own. On hand, not saleable, or just able to be used? Use possess. Don't care, and are willing to be a touch more informal? Use have, which is acceptable in almost all cases that own or possess would be.