Not to be picky here but I do have to point out that not all items have their own unique id per se. For example, if you have two of the same pieces of equipment and choose to meld materia onto only 1 of them and then set the melded one to a gear set, you'll quickly find that occasionally when you change to that gear set it will equip the non-melded version of the same item instead of the melded version that you actually assigned to the gear set. That said, it's more accurate to say that every item has a specific id that is the same for all versions of that item.
Even so, I would agree that servers and characters do have a unique id because if they didn't there would be a lot of security concerns on SE's side of things.