Howdy Y'all -
These "Networks" not only share software but they share tourneys and players as well. For example, you can log in through BET-365 and join a tourney yet be up against others who have logged in through Royal or any other Prima site. They do have room specific tourneys as well but those are pretty rare. Also, most sites within any one network share the same rules regarding deposit bonuses and withdrawal requirements and such.
For example, the Play-Tech sites GM mentioned host mostly R/A (Re-Buy/Add-On) tourneys yet Club Dice also has their own "CD Tour" which is site specific. In other words, you can't play the CD Tour from Noble or Fair like you can their typical tourneys.
I hope that adds to GM's explanation a bit and I wish you luck!