The words "own" and "possess" refer to material things. We cannot own friendship, for example. We may "have" friendship.

"Own" and "possess" are for concrete things. Eg. I own a car. "Have" can also be used with concrete things. Eg. I have a car. The meaning is slightly different though. To have in this case means "to be in possession of", not necessarily that it is "owned". "Have" is also used with non-concrete things such as an illness. Eg. I have a cold. You couldn't own a cold or possess a cold, but it is a state of being. The difference between own and possess are minimal. To be particular, you can possess something, but not own it. So, to possess it would be to have it with you. To own something would be to have paid for it, or to have rightful ownership. I hope this helps a little.

"Own" is much more common than "Possess", and "have" is probably a little more common to use than "own" when referring to owership. For example, I would say "I have a car" if someone asked me. I would say "I own a car" if there were some doubt as to if the car was actually mine and I wanted to clarify that it really is mine and I was not leasing it or borrowing it from someone else.