Heated Debate!!!
Actually, you need to heel and toe in order to double clutch, but they aren't the same thing. Heel and toe is operating the brake and accelerator with the same foot at the same time. Double clutching is clutch in - shift to neutral, release clutch - rev the engine - clutch in, shift to next lowest gear - clutch out and drive on. You accomplish this by heel and toeing.
In the olden days, synchros were poor or non-existant and double clutching was necessary to synchronize the gears to shift down. You needed to shift down going into a corner because your drum brakes were fading so badly that slowing yourself with the engine was your only option. So you were usually braking and shifting down (by double clutching) at the same time. Hence the need for heel and toe. After years of driving Moss crashboxes in XK Jags, I remember this well.
BTW, in North America its called double clutching, in England its called double declutching. Just another example of the two countries separated by a common language!
Double clutching is unnecessary with modern synchros, and slows your downshifts, even when done with skill and alacrity. Heel and toeing to blip the throttle while downshifting is essential to smooth downshifts. If you match the flywheel and gearbox speeds on downshifting, there's virtually no wear on the clutch. If you rely solely on the synchros and don't blip the throttle, you are using the clutch to accelerate the engine, which momentarily causes clutch slip and accelerates clutch wear.
Plus, done well, it feels and sounds great! /ubbthreads/images/graemlins/smile.gif