Each bitcoin is identified by a block assigning it to a key. Keys are not guaranteed to be unique, with enough guesses you can duplicate one (if you have some t

Each bitcoin is identified by a block assigning it to a key. Keys are not guaranteed to be unique, with enough guesses you can duplicate one (if you have some time before the heat death of the universe or so) and maybe win the lottery (i.e. access to someone else's bitcoins). So in all, things are more "very probably unique".