Welcome to the forums Garry,
It's an interesting question and not too surprising that you've asked it really.
Poker has been around for a while in the online world already and there are a number of poker sites that run off the same network. When players are with a particular website that's part of a network, as you say, they can play against other players on that network not matter what website they signed up with initially.
Online pool is not like that at the moment (poker wasn't like that about 4 years ago either). At the moment each of the main online pool networks have been built by the website themselves and it's only their players that can play on their own network. So, Play89 players and PoolSharks players cannot play against one another.
In time (maybe a few years?) I'm sure sites like Play89 will allow other websites to be a part of their network, that's when you'll see players from more than one website playing against each other.
Hopefully that answers your question
