Lucite is the highest grade form of acrylic and has an optical quality close to crystal. Acrylic and Plexiglas are brand names of similar products but different manufacturers. They are usually sheet products while Lucite is a hand cast product.
There are many different types and grades of Acrylic. Lucite is a brand name of acrylic that is used that has become synonymous with acrylic embedments. Plexiglas is another trade name of sheet cast or extruded acrylic.