Yes, that's the button, and those are the lights. It is true that the systems do not turn completely off with that button, if you really spin hard they will still come on. You can kill them and the ABS completely, 100%, by removing the fuse. I'm pretty happy with the "mostly off" TC, though, and personally I leave SC on most of the time.
My GF drove the Sonic in serious snow for the first time today; last year she wasn't a live-in GF yet, and the few times we went anywhere in snow I was driving. But yesterday she took the F150 in, and then had to struggle home with it. This morning I suggested she take the Sonic instead. Man was she happy about that! So much better traction and control than that big pig of a pickup. Now admittedly some bags of sand in the back will help the truck.... but she'd still rather take the Sonic if it looks at all scary out now.