Powdered sugar is a very finely ground form of sugar that is synonymous with confectioner's sugar. In Britain it is often called icing sugar. It is used principally to make frosting, icing and other cake decorations. It is often lightly dusted onto a baked good to add light sweetness and subtle decoration. It is generally mixed with cornstarch or flour, to improve its flowing ability. Therefore, it can't be used to sweeten a beverage, for example.
Caster sugar, generally unavailable in the United States, is slightly less finely ground and so is less "powdery".