Huge difference.
Buzz Lightyear, of course, is older. The one at WDW has big guns, mounted to the ride car. They're somewhat difficult to aim. I can never locate my laser beam. Guests can rotate the ride car with a joystick to get better aim. It's a space theme (obviously) and your "mission" is to shoot the Zs and defeat emperor Zurg.
TSM is new, is a creative juxtaposition of cutting-edge technology and classic midway games. Guests wear 3-D glasses and use pull-to-shoot guns (which are so much easier to shoot) to play 3-D games. You weave in and out of the midway area and play a variety of different games.
I personally enjoy TSM a lot more (even though my sister beats me on TSM and I always beat her on Buzz). It's so much more interactive. You can't see the other players during each game, so it's a lot more personal (you can see them through screen transition, though). It's also so much easier to tell the difference between your gun and your partner's gun (one red, one blue), as well as easier to tell what you're aiming for and whether or not you got it.