It's the current delivery capacity that hurts. I= current flow, E= voltage potential, and R= resistance to current flow.
I=E/R The wet tongue is about 1000 ohms of resistance. Braces are, for this purpose, 1 ohm of resistance.
Solve for your tongue. I=9/1000 or .009 amps or 9 milliamps, won't even feel it.
Solve for your braces. I=9/1 or 9 amps or the maximum that the battery is able to deliver to a short. Now heat produced in your braces is P=power, P=Isq x R or 9 x 9 x 1 or 81 watts of heat. 2 watts will burn your skin. Put that much heat on your most sensitive nerves, your teeth, and that, my friend, hurts.
A car battery would have produced about 12 amps which would have fused the braces and turned them molten. :shock: