I think there is some confusion here about exactly what an "e-diff" is. This term was first used back the day when the 135i was introduced in 2008. That car had an open differential, but used the rear brakes to brake individual drive wheels if there was excessive spinning of one of the drive wheels, which then directed torque to the other drive wheel which presumably had more traction. This reactive system tried to mimic the effects of a mechanical differential, but obviously is not as good. Even my 9 year old C55 has this system.
Then came the Ferrari 458 with another "e-diff". This is different. This car has an mechanical multi-clutch limited slip differential, but the amount of "lock" was controlled electronically. Because of the much more variation in the amount of "lock" that is available and controlled by an ECU, this system is superior to the classic pure mechanical limited slip differential.
My GT3 has a similar system (electronically controlled mechanical limited slip differential), and I must presume that the C63 S has a similar type of setup, while the standard C63 has a simple mechanical limited slip differential with no electronic control.
Torque vectoring is something completely different. Here the brakes are used ACTIVELY on the inside drive wheel during cornering to increase the "yaw" or rotation of the car to make turn-in more efficient and effective.