There's no confusion in my mind, and there shouldn't be in yours. Either something belongs to you, or it does not. If you find something that does not belong to you and you keep it, then that is theft and it is wrong.
The only issue is, from a pure practicality point of view, it's just not worth taking 20p to the police station, so I would not bother, and nor would the Pope.
But if it was a serious amount, I would hand it in.
You say "That is to take something which is in the possesion of someone else though, whereas as finding a fiver on a curbside or a bag full of money with no-one in sight, is not stealing."
Yes, bud, it IS. The fact is it belongs to someone and that someone is not you.
What about my camera on a beach towel example? Would you take that? Like the bag of money, you don't know WHO it belongs to. And you aren't going to get caught. There's no-one around. It's dark. They have shut down for the day. My guess is you'd nick that as well. I would not. And it has nothing to do with whether you would be caught or not.