RAILS
The side edge of the board.60/40 Rails seem to be the more popular because of the extra wave gripping power. 50/50 rails provide quicker release so turns can be accomplished with less effort. Concave rails are a bit more technical. With surfboards and other craft that have rounded edges, the water flows smoothly over the rails, with no friction or anything. With 50/50 rails (or any rail with an edge) the water will try and flow along a smooth path, but when it hits the flat edge, the water must try and stick its flow to the shape it is going around, just like when you hose something on an angle, the water will not just fall straight off, surface tension will force it down the angle. So after seeing that the suction came from this angle, it was thought maybe if it becomes concave, the suction will be greater still. Some argue it works, some aren't convinced. Some body boards seem to be acquiring concave rails towards the back. The idea is that these things stick pretty well in tubes. In steep tubes the back corner of the board is about the only thing in the wave.
BOTTOM DESIGN
Since this is where the most water flows past the board, the most effect is done by altering the design of the body board here. The vast majority of boards have slick bottom skins (which appear to be made from plastic).These decrease the resistance and therefore increase the speed when compared to the older foam skins.
Flat Bottom - This seems to the most popular bottom configuration. The flat bottom allows easy maneuvering and the ability to do tricks such as spins with little or no resistance.
Tunnel Bottom - This allows water to move around 260 degrees of rail, giving good wave holding. These types of bottoms excel on fast straight waves.
Concave - This is similar to the tunnel bottom, but with slightly less grab into the side of the wave. The transition from rail to rail in turning is smoother as the rail inside edges are not as sharp.
Channels - Adapted from the surfboard, channels make the board hold better to the wave. The downside is they make the board easier to skate from rail to rail.
Dimples - The new wave of golf ball style bottoms are designed to reduce the friction on the bottom of the board, and make it ride on a cushion of turbulence.