I recently went through the 3 vs.4 wire question while wiring up my air-compressor. My local home depot left alot to be desired in terms of electrical professionals on staff(I'm not one either!). When inquiring about a 4 wire vs. 3 wire I got varied answers and all over the map and most said by "code" had to run a 4 wire set up and had to hook up all 4 wires to the compressor. At the end of the day, choose to purchase a 4 wire 8 gauge and ran 20 ft cable in flex conduit to my 5hp 21amp compressor(see reasons below). Also installed a 50amp breaker as starting the electric motor pulls a higher amp draw before settling down to its run state of 21 amps which is what my electric motor is rated. If running a length of cable from your electrical panel to air-compressor across the garage, make sure you use a heavy enough gauge. For shorter runs I could have used a 10 gauge wire. Since I was running 20-25 ft went with a 8 gauge wire.
I hooked up the following for my air-compressor install:
Red-hot, black-hot, green-ground. No white-neutral was used).
Within my compressor switch box located on the unit itself, I hooked up 1 hot wire-black to the shut off electrical bus-bar, 1-hot wire-red to the electric motor wire, and 1 wire-green to chassis ground. Again, no white-neutral used in my set up.
Purchased a 4 wire cable vs. 3 wire so that in the future if I wanted to hook up 1-hot wire and 1-neutral-white from my extension cable that would give me 120v for adding a lighting fixture near compressor, coffee maker, whatever. Figured I'm going to run and install the feeder cable myself one time, might as well run a 4 wire and be done. Also incorporated locking twist lock 50amp male/female connectors so that I could disconnect the power at the air-compressor location at any time and plug in a 220v welder some day, then switch back when air is needed,etc.
If interested in some pictures, I can start a new thread regarding my compressor and air-line install.