Yes, the 3rd speed switches the batteries from 12 to 24 volts. It takes both the B and C contactors to do that, and that is why the switch on B turns on C also. The A contactor bypasses the resistor. So 1st speed is 12 volts, and going through the resistor. 2nd speed is 12 volts, no resistor. And 3rd speed is 24 volts.
Since the batteries are being switched from parallel to series, it can cause high speed problems. If one of the batteries or connections is bad, it will run ok in 1st and 2nd because there is 2 sets of 12 volt batteries. But, when in 3rd speed, all the batteries are connected in series and if one is bad, or a cable is bad, you get nothing. There is also a fuse that if blown won't let the batteries connect in series for 3rd speed.
All the switching of the contactors is done with switches in the control handle. The turtle/rabbit just shuts off the 3rd speed and the machine stays in 12 volt mode.