Mhhh, as far as I understand its like this:
CTT: A few players are invited. Aim is to test the servers, online playability and to let things crash due traffic to see were the weakspots are. Its not actually about bugs and glitches, more about the availability. When the game+servers+shift can handle it they´ll open a Alpha/Beta.
Alpha: More people get involved, tracking minor bugs, unbalanced skills, ect. Basically to find the problems the devs and companies testers did not find.
Beta: Even more people involved/sometimes only Alpha-players involded. By hat point many games already developed a “meta-game” made up the behaviour of the players. This is an important step in a games evolution and most interesting to devs. Further bughunting, glitch-reporting and skill-balancing.
Don´forget about Opened- and Closed Betas/Alphas… its all a mess^^
As far as I see all thee types include tests of how many people the servers can handle. Remember the times Diablo-3 servers got flooded here in Europe or WoW with its great waiting lists… The CTT will show if BB can handle all testers as once and where the system might crash.
All only my experiences^^ I saw another member explainig it very well, but I can´t find the post anymore ToT