awk - Yeah, tt is flat-track racing. I think that a rear shock set up for tt is a lot stiffer than stock. When racing flat track, you want as stiff a shock as practical, to help keep the rear wheels firmly planted on the track. Many old race bikes were actually hardtails for this reason.
When you're MX riding, the shock has to work hard to absorb bumps, so an MX shock has a lot more piston travel than a tt unit. It is often equipped with dual-or triple-rate springs to prevent bottoming-out and improve rebound.
If you're thinking of putting a tt rear shock on a trail Blasty...I've never done this swap before, but if the shock mounts up and can stand the rider's weight, I'd say go for it! You will probably find that the rear suspension stiffens up considerably, and you may see better traction and tire hookup.
That being said, I would not hit any hard bumps with a tt shock. A tt shock is designed for track performance, so it may be damaged if the trail riding gets too crazy...