While there is no real way to answer this, one can get a feel for it.
For the most part, it all starts with the World Confederation of Billiards Sports (WCBS), the governing body for all cue sports in the world, including pool, snooker, billiards, etc.
Governing bodies of the individual sports are accountable to the World Confederation of Billiards Sports, and in the case of pool, the governing body is the World Pool Association (WPA).
National and multinational pool organizations such as the Billiard Congress of America (BCA), the European Pocket Billiard Federation (EPBF) and the Asian Pocket Billiard Union (APBU), and others, fall under the umbrella of the WPA.
There are national tours and regional tours that report in to organizations like BCA, EPBF and APBU. In some cases, there are independent tours unaffiliated with these organizations. the most famous independent tour was the IPT in 2006-07.
…. and so on and so on and so on.