As far as I understand it, different clients use the same network (and therefore some of the same games) which is why you can only run one client at a time on one PC (although there are ways around this).
So some of the games on one client are exactly the same games as you can find on another client and you can use either client to access the game on the network. The reason why you can see the same names is because your client nickname is actually an iPoker nickname.
Essentially, if you have two client nicknames then you have two iPoker network nicknames, but the network doesn't care about what client you use to access it. The game is the same game regardless of what client you are on - the nicknames you see could be using a different client to you and you can access the game using whatever client you wish.