Some of it .. I swear is confused just to be confusing...
Taps that serve potable water, are Faucets in the North, Spigots and the South, but those that provide water not fit for drinking are called Spigots in the North and Taps in the South.
I'm from the Pacific Northwest and I've exclusively heard "Faucet" regardless of potability or indoor/outdoor use. (Spell checker doesn't think potability is a word, but it totally is.)
"Faucet" on my kitchen sink.
"Faucet" outside that I hook my sprinklers to.
"Faucet" connected to a well.
"Tap" on a beer keg.
"Spigot" ... not used around here, but I'd think "Faucet" if someone actually said it.
We also use:
Drinking Fountain = Faucet that emits water upwards a few inches that lets you drink directly from the stream (or fill a bottle). Usually includes a basin to catch the water that you don't drink/bottle.
Fire Hydrant = 'Serious business' water supplies placed along the sides of roads that fire-fighting vehicles can connect to for high-volume, high-velocity water near the scene of a fire.