I believe player ranking on the Azbilliards site is based on how often that player's profile is visited, it has no basis on skill. There is also the money ranking, which you could say is loosely based on skill, but not entirely accurate.
A world champion would be the winner of any of the various world championship tournaments that are held. I believe that the currently held world championships are 9-ball, 10-bal, 8 ball, and straight pool (and trick shot if you want to include that).
