So, in this picture, the item on the left is the lower turntable assembly from a Sony HIL-C2EX Hi-Vision LD player. The one on the right is the corresponding part from a Sony MDP-455 LD/CD/CDV player. The difference in clamping area speaks for itself, I think!

The difference is one player plays CD's and the other doesn't. All LD only players have the larger grip surface, even the newer Pioneer players