Most of the games sites which have pool available as a game to play are either part of a network or they have all their own players. As a network games sites can attach more than one site to a specific game so different people will be playing against each other from different sites. Usually on this network games site the player is unaware that they are playing against people who are from other sites.
The main reason for a networked site is to allow more players to play against each other or, in the example of playing online pool, more options to play different tables one-on-one with different pool players. The 'liquidity' of a games site or how big it's base of players is is important when selecting which site you would like to play at. A network pool game site which allows the chance to play online pool is likely to have more players you can choose to play against. A stand alone games site which has online pool games may only ever have a few players online at any one time who you can play against. Choose wisely which games site you play with. Networked online pool sites can offer much better alternatives.