Minecraft wiki entry for Minecarts, associated text: Rails always have to sit on another solid block and are the only rail type that can curve.
Detector rails give off a redstone signal when a cart passes over them, otherwise they act as a regular rail.
Powered rails add momentum to a cart passing over them when powered, when unpowered they have a braking action and slow or even stop a cart.
Activator rails trigger an action on a cart passing above them when powered: TNT minecarts are set off, a hopper cart gets deactivated, and players/mobs riding in one are pushed out of it.