Well on my 2009 335xi the AWD is on even when DTC/DSC is full off. Car will spin all 4 wheels on ice and do donuts. On mid-2008 and later, even the e-diff on 2wd models is not off when DSC/DTC is off. AWD part of DSC on Xi is like the e-diff, it brakes individual wheels to simulate LSD across all four wheels and it cannot be turned fully off.
DSC cuts engine power and uses individual brakes + transfer case to implement traction control, skid control, spin control.
DTC leaves engine power alone and lets you get some wheel spin and a little tail happy, but too much tail out and it kicks in to stop it. You cannot do donuts with DTC on.
DSC/DTC full off keeps basic AWD on in the sense that it sends power to single spinning wheels or axle via fake e-brake or transfer case but no wheel spin control (if all four wheels spinning same rate) or chassis stability control intervention. No engine power cuts. So for example DSC/DTC off if it sense rears spinning and fronts not will still send power to the front axle and lock up TC, same if it senses one side spinning and the other not (modulo steering input) but if all four wheels turning same rate it does nothing.