spread option is a generic term for the new brand of option football, back in the day option football was like Nebraska with Eric Crouch, its what Navy and Air Force runs. The spread part is because most teams use 3 to 4 receiver sets. You could say the Patriots use a spread offense Although spread also kind of meant to literally spread the field with linemen lining up further apart, the idea being that the defensive ends are further away from the qb but teams vary on how wide the linemen line up.
Basic zone read is leaving a defender unblocked usually the de, allowing the offensive line to get good double teams, if the unblocked defender comes after the qb, he hands off, if he comes after the rb he runs. It has evolved and there are many wrinkles since there is a way to stop the basic zone read.
pistol formation combines the benefits of lining up in shotgun with the benefits of having a downhill running game like the i formation or single back sets. The spread option has had problems with power running out of shotgun, Florida combated the problem with having Tebow run up the middle. Nevada came up with the pistol formation, so your rb is going downhill when taking the handoff. The qb lines up 4 yards behind the center and the rb 3 yards behind the qb, in shotgun the qb is 5 to 7 yards with the rb more to the side. I've never understood why more teams don't adopt the formation, its not that big of an adjustment, usually in the NFL the qb is only 5 yards back in shotgun.
It makes things easier on the qb because they crowd the box for the run, they have to worry about the qb or rb running and the qb passing, it usually gives the qb single coverage when passing. A good deal of college defenses have gotten used to it and have found ways to slow it down. Although every couple of years they add some new wrinkles in that makes it harder to defend with guys like Chip Kelly usually staying ahead of the game. This is the first year the NFL has had to prepare for a full spread option attack, with Washington's being the most complicated, Shanahan mixing in his potent zone blocking scheme in with the spread option.