Sugars vary in color from white to dark brown depending on the amount of molasses added during processing. The size of the sugar crystal affects the amount of air that can be incorporated into the batter during the creaming of the sugar and fat. For example, granulated sugar will incorporate more air into the batter than confectioner's sugar. The size of the crystal will also affect how quickly the sugar will dissolve in the batter. Therefore confectioner's sugar will dissolve quicker in the batter than granulated sugar.
Granulated sugar has small granules and is the one most often used in recipes.
Try to find one where the crystals are not too large as they do differ from manufacturer to manufacturer. You can make your own by processing granulated sugar in your food processor. They are typically used for garnishing baked goods. Crystal sugar is like coarse sugar except the crystals are pellet shaped. Confectioners sugar is granulated sugar that has been ground to a powder with cornstarch added to prevent lumping and crystallization.