The two types commonly found are mat and cloth.
Fiberglass mat is the stronger of the two, able to maintain strength over big, open surfaces as well as complex curves and other shapes. It derives it's strength from the randomness of the fibers. There is little to no directionality in what little flexibility it has, so there is less of a chance for stress fractures from normal wear and tear. While it is stronger, it's also a little more difficult to work with than the cloth. If you are unaccustomed to fiberglassing, you'll likely end up with more of the fiberglass mat on your gloves than the item you're glassing!
Fiberglass cloth is the weaker of the two, but for costuming purposes it works just fine if you double up your layering (or even triple layer your work). It is the same exact material as the mat version, except that it has a woven, geometric arrangement to it instead of a random arrangement. The geometrical nature of it allows it to have a slight flexibility to it along it's grid axis, which can cause minor stress fractures if the part is significantly impacted. To combat this, multiple layers in alternating directions is recommended.
I prefer using cloth for most parts (including helmets) because it's a little less stressful to work it. However, if there is a larger or thinner part protruding from the body of my work piece, I'll use fiberglass mat on that portion, and especially along the joint to that piece. For most applications here, cloth works fine, but you may wish to reinforce certain areas with mat.