I'll try to give you the Cliffs Notes version. Understand, though, that like so much of the "complexity" that people are fond of attributing to football, it's mostly semantic in nature.
Regarding the pistol
: There is a formal pistol offense in college ball, but I have a hard time thinking of it as anything more than the latest permutation of the option offense family. To my mind, the pistol is more usefully thought of as a formation that places the QB midway between under center and the shotgun set. A pistol is smaller than a shotgun, get it? In brief, you retain many of the benefits of the shotgun while making it easier to reliably run running plays. That's the quick and dirty version. A bit of googling will get you knee deep in however much complexity you desire.
Regarding the option
: There are about 3.6 trillion iterations of the option. It's a much more formal family of offenses than the upstart pistol, and while the pistol is defined by its core set, the various flavors of option tend to have their own unique sets, ie wishbone, flexbone, spread, etc. Let's steer clear of the semantic morass regarding the types of option offenses and concentrate on its core concept, that is, giving the quarterback the "option" to react to the defense after the ball has been snapped. In the option, the ball is snapped to the QB and he then reads the defense. Based upon what the defense is doing, he then either hands off the ball to one or more running back options, or hangs on to the ball himself. Traditionally, the QB runs the ball when he hangs on to it, but newer iterations have sought to give him viable pass protection and routes to pass to.
The chief benefit of the option is that you get to read what the defense is actually doing, rather than anticipating what you think the defense will do once the ball is snapped. The downside is that option plays tend to be a bit slower developing and they do expose your QB to injury.
Anyway, that's the quickest and dirtiest explanation that I can come up with. I've left a lot out that others can get into, also a bit of googling will surely get you more than you'll ever care to know about the various options.
I hope this was helpful.
[ Edited by BubbaParisMVP on Dec 30, 2012 at 7:31 PM ]