Granulated sugar is pure sucrose, chemically the same as superfine (also known as caster or castor) sugar. The crystals are not as fine though. Typically one type may be substituted for the other.
Superfine sugar more easily dissolves in cold liquids. This can help to make meringues of a finer texture. In some cases, this property is undesirable. For example, the coating on Saucepan Fudge Crackle Cookies is specified to use regular granulated sugar; superfine sugar might dissolve.