DSC remains on when DTC is activated either by enabling SPORT+ or by pressing the DSC button once. SPORT+ automatically enables DTC so you can get tail happy, but DTC's other function is to provide a greater slip threshold on looser surfaces where momentum is key. If DSC remained on in full force, the car would instinctively cut power and apply the brakes when slippage is needed. This loose threshold, combined with default COMFORT mode (the car calls this TRACTION mode), provides for more dramatic weight transfer/squat (think: putting sandbags over the powered axles) and allows you to make more deliberate throttle inputs to get yourself out of a ditch, snow bank, or up wet/slippery inclines. (Note: if you do not have the adaptive suspension, COMFORT only applies to throttle response). DSC OFF, which requires that you hold the DSC button for a number of seconds, puts everything in SPORT and leaves managing the car's dynamics up to you.
This is why SPORT+ is simply SPORT with DTC enabled. If you press the button for DTC in SPORT or COMFORT, the car will go into TRACTION mode. But SPORT+ is the only way to turn DTC on without enabling TRACTION mode. So you can think of SPORT+ as power slide mode.
2001 Audi A6 Allroad 2.7T (C5); 2005 Audi A6 4.2 Quattro (C6); 2005 BMW X5 4.4i (E53); 2008 BMW 535xi Sports Wagon (E61); 2011 BMW X3 xDrive35i (F25); 2009 Audi A4 3.2 Quattro Prestige (B8)