BMW have nicely made this as confusing as possible.
'Dynamic Drive Control' is the rocker switch which allows you to chose between driving modes, firming up throttle response, steering feel and gearbox mode. This is fitted to either:
a) A car with the Sport Automatic Transmission option
b) A car with the Adaptive Drive option
c) A car with the Dynamic Damping option
d) A car built after September 2011
'Dynamic Drive' is the active suspension system which uses active stabilisers to control bodyroll.
'Dynamic Damping Control (or VDC, Variable Damper Control) is the electronically adjustable suspension which allows you to change the firmness of the suspension.
'Adaptive Drive' is an options package which combines Dynamic Drive and Dynamic Damping Control/VDC together.