Plexiglas and fiberglass have names that are similar, but in reality the two materials are quite different and suited for vastly different applications. The only real relation between the two products is their relationship to glass. Fiberglass is a special type of plastic strengthened with actual glass. Plexiglas is a totally synthetic product that was developed as an alternative to real glass.
Fiberglass is produced in a number of different forms, each suited for specific applications. Sometimes, it is spun into thin threads or batting and used as the insulation in homes. In other cases, it is formed in cloths of varying textures and thicknesses that are used in fiberglass fabrication. The cloth or other material is shaped and mixed with a resin that hardens the combined materials into the hard and strong fiberglass shell.
Plexiglas is actually a very common brand name for a product that is made from acrylic. This is a petroleum based plastic product that is translucent like glass but doesn't have the safety risks that glass does. It is considerably stronger than real glass, doesn't shatter the way that glass does and is also half as heavy as an equivalent amount of glass.
Both fiberglass and Plexiglas have the potential to be very strong materials. When made thick enough, fiberglass is used to make car bodies and the hulls of boats. The type of fiberglass material and the resin used also impacts the strength of the material. Plexiglas is made in varying strengths and treated with different products to support the base material, and can be made thick and strong enough to stop a bullet.
Deciding which material is best in a given situation depends largely on how you need to manipulate the material. Once you buy a Plexiglas piece, there is very little you can do except cut it to size. Fiberglass, on the other hand, is an extremely flexible material, because you can shape the sheets or strips to any shape you desire. The flexibility of fiberglass is one reason it has been used in the creation of car bodies.