the difference in terms of procedure, or the difference in terms of what is happening with the layshaft/synchros?

Here's the procedure for a double-clutch:

double clutch downshift:

1 - in 3rd...clutch pedal in.
2 - shift knob to neutral.
3 - clutch pedal out
4 - rev engine to match car speed
5 - clutch pedal in
6 - shift knob into 2nd.


double-clutching will match your layshaft speed with the gear speed, putting less work for the synchro's, as well as matching the engine speed.

rev-matching alone will match your engine speed, but the synchro's will still need to do its work to match your gear speed and layshaft speed.