Biggest difference between the 'Shoot and the Air Raid variant that TAMU runs is that the true 'Shoot is exclusively a four-wide formation offense. A true Run and Shoot will always line up with four wides, either 2 x 2 or 1 x 3. No tight ends or fullbacks whatsoever. And as others have mentioned, there are a lot of "option" routes that give the wideouts freelance ability. The original offense always featured the QB taking a sort of half-roll from under center, but the modern variant is mostly run from the shotgun or pistol with typical drop-back passing.
At the FBS level, June Jones at SMU is the only coach I know of that still uses the 'Shoot, and his version has morphed considerably over the years. There are a handful of teams that incorporate some 'Shoot principles...ironically enough, one of them is Georgia Tech - a flex option team. Their base "flex" formation from under center is basically the original Run and Shoot formation, with two wides and two "wingbacks" set up 2 x 2. Paul Johnson has been on record saying that they run some 'Shoot concepts, and if you watch cut-ups of Tech's passing plays they are very reminiscent of the original offense.