Grapeshot,
BJT did an excellent job of describing Western 3-Gun! The best I can do is offer a few minor/finer points. First there are fewer shooter categories. For example there is only one Duelist category rather than many.
He mentioned that a pump shotgun can sometimes be stoked with four rounds with the hammer down on an empty chamber -- that is in the Open category. Shotguns are typically staged horizontally on a flat surface such as a table or "bar". They are loaded at the place where they are to be staged, and only after everyone (spotters, painters, target resetters, etc.) has cleared the downrange area. "Clear to load" is the statement I've heard from the RO's in this regard.
A key difference from SASS, other than the obvious one, is that there is no such thing as a Procedural. BJT touched all around this, but didn't say it outright. W3G offers the shooter a lot of latitude in deciding which targets to shoot when, as long as they do it safely. This is one of the things I enjoy most. As anyone who knows me can verify, I don't always think like other folks, and as anyone who has ever shot W3G with me can verify, I often don't shoot a stage the way most others do.
You will hear folks -- most of whom have never attended a W3G match -- describing W3G as a "run-and-gun" sport, implying or stating directly that it is inherently hazardous. Nope. Safety always rules supreme.
I shoot both SASS and W3G, and each has its strong points. Neither, IMHO, is "better" than the other. If I could only shoot one or the other, I' probably pick W3G, but then I've already told you about the way I think!

Hope this helps.
-- Nighteyes