I am not sure what you call caster sugar but we have 3 types of white sugar
normal granulated the coarsest one
caster which you use in cooking for sponge cakes
Icing (powdered) which you use for dusting cakes or making icing
From Q Chef:
>>> Castor or caster sugar is the name of a very fine sugar in Britain, so named because the grains are small enough to fit though a sugar "caster" or sprinkler. It is sold as "superfine" sugar in the United States. Because of its fineness, it dissolves more quickly than regular white sugar, and so is especially useful in meringues and cold liquids. It is not as fine as confectioner’s sugar, which has been crushed mechanically (and generally mixed with a little starch to keep it from clumping).>>>