Commonly available processed clay types fall into the following broad categories.
Earthenware is nonvitreous pottery that has normally been fired at relatively low temperatures. Non-vitreous means it may be still porous and not watertight.
Midfire clays are formulated to provide some of the strength of stoneware whilst not being fired as high.
Stoneware fires at a higher temperature. It produces hard, strong pieces that are vitrified and very functional.
Porcelain is a particularly white fine and translucent body that usually in the same firing ranges as stoneware. It is made from ball clay, china clay, silica, and feldspar. Originating in China, it has traditionally been prized for its whiteness and purity.
Paper clay has paper fiber added to the clay body. This makes that clay stronger as it dries and allows the clay to be worked in ways that are not possible with non-paper clay bodies. Paper clay can be hand built, thrown, and moulded. The paper content will burn out in the bisque firing.