Listen up:
The car behaves completely different from one mode to the next.
This is no hoax, and I don't know why Mazda in their infinite wisdom (did I mention my F-ing engine fell out of my car!!?!) chose to do it this way, but if you drive the car in each mode, it will become apparent to you, too.
Take the car out to a race track and try each mode. A couple have tried this, and discovered the car is faster on the "full off" mode compared with the other two. Why? I assume its because the "full off" mode provides ZERO computer intervention compared with the other two, and as such you can rotate the car around and get it to slide around a bit, which is beneficial on a closed-course race track.
To reiterate:
Leaving all systems nominal from KOEO (Key On Engine On), you have full traction control, as well as full dynamic stability control. Both of these can be proved to be functional by either trying to spin the tires, or by pulling the E-brake. You'll quickly notice that the car is in control of YOU.
Press the DSC switch while the car is running, and you'll now have traction control removed from the game. You can spin the tires at will, and the car will not intervene. However, you if you pull the E-Brake during this mode, the car will regain control. As will it if you pull an aggressive trail-brake maneuver.
Now, with the car fully off, press the DSC button before turning the key and starting the car, and release shortly afterward. With this mode, all nannies are off, and you could easily spin the car if that was your wish through maneuvers. The tires will spin at will, and the brakes independent of each side of the car don't do what the DSC system tell them to. The system is fully disabled.
No matter what you believe and what you don't believe, this is how it goes according to the results I've seen.
**Edit**
If you think this is law-suit worthy, then how about an engine falling out? Or, lets take it further, and say that GM owes me money because they taught me how to spell "Gauge" wrong. All their cars spell it "Gage". I want money. LOL