Advice! - Where at all possible, use the Mental Ray renderer and photometric lights with raytraced shadows only. This will give you the ability to create realistic scenes far more easily. It will keep your scenes simple and easier to manage!
Shadow Maps These are bitmaps that the renderer generates during a pre-rendering pass of the scene. Shadow maps don't show the colour cast by transparent or translucent objects. On the other hand, shadow maps can have soft-edged shadows, which ray-traced shadows cannot. (unless you use a mr light whose source is anything other than a point).
Area Shadows These simulate shadows generated by a light with area or volume. Not supported by the mr renderer.
Ray Traced ShadowsThe mental ray renderer can generate shadows by ray tracing. Ray tracing traces the path of rays sampled from the light source. Shadows appear where rays have been blocked by objects.
You can use shadow maps instead of ray-traced shadows with the mental ray renderer. This can improve performance at a cost of accuracy.