With the clutch engaged (pedal out) and the transmission in X gear; engine, transmission and driven wheels are all connected, spinning at given speeds for RPM and ratio.
Clutch disengaged (pedal in) and transmission still in gear; engine disconnected, transmission and driven wheels still connected (which means the engine can be made to spin any speed, transmission is being spun by driven wheels at X ratio).
Clutch disengaged and transmission in neutral; all three disconnected (which means engine can be spun any speed and transmission will spin freely).
Clutch engaged and transmission in neutral; Engine connected to transmission, driven wheels disconnected (which means engine speed determines transmission speed: use engine to make transmission speed match new ratio to driven wheels.)
Now, to answer your question about missing anything...
As a normal driver, double clutching is most likely a waste of time and effort, and actually puts a little extra wear on the clutch and throwout bearing over just rev matching.
Also, people who are good at double clutching can do it quicker than you can excecute a normal shift, mainly because they are race drivers and have to out of nescessity.
It is easier to just hold the clutch and match revs, but in racing, you have to do that while braking, which is what heel-toeing accomplishes. Double clutching comes down to personal preference. I mean, synchros were invented so we wouldn't have to double clutch any more so why save them from having to do their job?
Now, it seems like theduker is getting ready for a flame. I'm not going to shoot fire, but I am going to send a few sparks his way:
Yes, trying to heel-toe in normal driving is a good way to slip your foot off the brake and rear-end somebody, and to brake and then rev match is a slow way to go about it, but his comment about "This won't win you any auto-cross races" is contradictory because you don't have anybody to run into on an autocross, so you wouldn't have to worry about it, and being good at heel-toe downshifting gives you the edge that is the key to auto-xing.
I'll happily hand any clown in a V6 ATX Altima his a** at the finish line because I can drive my SVT better than he can ham-fist his Nissan. If he does beat me, it'll be because he's a better driver. Auto-xing is about driver skill, not hardwear.
Peace be with you all
Jed