APA and BCA are similar, but the main difference in them are the way the game is played and the rules that they use. On the APA league all of the players have their own rank depending on how well they play the game, each team on the league can only have so many good players. When on a 8 ball team you will be ranked from a 2 (beginner) to a 7 (very advanced player). Each team are allowed to play 23 points per night. 9 ball teams on APA are allowed to play twenty-three points as well, but they are ranked from a 3 (beginner) to 7 (very advanced).
{On a BCA team the players are not ranked, so they can have as many good players as they want. So some teams in BCA have all excellent players while other teams might have all beginners, so there is not really any chance that those beginners will win much. On the other hand being a beginner and playing against an awesome team can also help you make your game better. The BCA league is more for expert players while the APA league is for fun.
The BCA league allows you to call a safety, that means you can take your shot regardless if you make it or not, you can give ball in hand to the other player, the APA league will not let you do that. On the APA league you do not have to call your pocket, in BCA it is required. When you break the rack in APA and if the 8 ball goes in the ppocket, you win but if you do that in BCA that is not a win. That is just a couple of the differences in the two leagues.