I think you're getting confused on the wheels.
Chin Spins and Flying Saucers are made large enough for a chinchilla to fit inside of comfortable and stretch out when running because they are at least 15" in diameter.
The wheel you have can hurt a chinchilla because while he is running his toes can get caught in the mesh, his tail can get caught in the bar that goes across the middle and it is only 12" which is too small for him to comfortably stretch out when running. All 12" wheels have this problem with not being wide enough for the chin to spread out when running.