Merge, Cake and some other smaller 'networks' provide a service. That service is providing a pooled game and includes the software running that game.
Lets use Merge as the example. Merge provides the computers and software, and network accessibility, and its 'Skins' (Carbon, Hero, Players Only
, SPortsbook, Lock etc etc) provide the player control. By control think documentation and authentication, and account control. These skins then open the door to the Merge games.
A pooled game is where players in one skin will sit down and play against players from any of the skins. Same table, different Skins in each seat.
Easier way to think about is is a large round poker room with a lot of different doors. Each door is a different 'Skin' and has some of its own unique entry requirements, and exit requirements (withdrawals).
Once in this round poker room, you sit at the same table with someone who entered via a different door.
Since the software (Merge controlled in this case) is showing the player names, it can not allow you to play against yourself. And for accounting reason your player name via one skin can not be the same as your player name via another skin. SO the large group of player names is controlled by the software (merge).
Cake works the same way, as does Zen (cheap cheezey software, with real time advertising and TV frequency Commercial breaks).
A small network thing perhaps even easier to understand is Cereus. Only 2 skins that I know of (Possibly ClubWPT, but unsure).
Absolute and UltimateBet play pooled games. You logon to UB, and sit at a table with AP players.
One of the things I have always wondered about with skins is...when they show how many players online / at tables, are they showing total network numbers or are those numbers only showing how many are from that skin?