I don't suppose the search button works very well on this subject since people call it by so many names.
You have DSC on the car which is the nanny state, stopping power to the wheels and flashing it's little light at the slightest excuse.
Pressing the DTC button briefly puts up the DTC light on the dash. All this does is delays the onset of DSC by a certain margin. If you like, it will tolerate more wheel-spin before "applying the brakes" so to speak (cutting engine power to the rear wheels).
Holding the DTC button in for about five seconds switches DSC off, almost entirely (in extremis, it will still operate) which means lots more wheel-spin tolerated with a concomitant reduction in safety which has to be replaced with driver skill. With DSC totally off, it can be surprising how dodgy the car can feel, you can't just drive it the way you would with DSC operating.
With snow, the full DSC comes on so easily you often find you can't move because the moment the wheel slips it cuts power and this is not what is wanted. But if you are sliding all over the place with virtually no grip at all, even when you have switched DSC off, it will operate when things get bad enough - hence the flashing light.