Caster sugar is more fine than the regular stuff and less fine than powdered sugar. You need it in recipes where it should dissolve quickly and evenly (no graininess and no clumps).

Regular sugar is called granulated sugar (mentioning this because if you're baking, this term comes up a lot). Put regular sugar in a grinder, the resulting powder you get is called caster sugar. This is used in recipes where you need the sugar to dissolve quickly. You don't have to buy it. If you have regular sugar and you have a grinder at home, that's basically all you need. To make icing sugar, you need to put granulated sugar + cornflour in the grinder. This is used mostly for icing and frosting only, so don't use icing sugar in a recipe unless specifically mentioned.

I'm making a new comment to answer, since I can't attach a picture otherwise. Icing is all the creamy decoration on top of a cake/cupcake. Like the white swirly stuff on top of this cupcake (This is a Google picture, I didn't take it)

It's warm here in Durban 😉

Icing sugar is granulated white sugar thats been pulverized to a powder and mixed with a small but mighty amount of cornstarch.