The answer to this question is "yes and no"!
Caster sugar is fine granulated white sugar. Granulated sugar simply means it comes in small crystals - if the recipe calls for granulated sugar, it usually means, quite simply, white sugar (as opposed to brown sugar or raw sugar - both of which are, strictly speaking, granulated sugars also). I often use caster sugar instead of granulated (white) sugar - it tends to dissolve faster and I don't think there's any situation where a coarser granulated sugar (ie "white sugar") would be better. Someone else might disagree!
Hope this helps!