Demerara sugar is unrefined, usually somewhat coarse but dry sugar. It is not brown sugar, which has clumps together. It is pale golden in color and can be called either raw sugar or turbinado sugar in the States. Caster sugar is a very fine grade granulated sugar, most often used for baking as it causes cakes to rise better, or for putting on fruits and berries as it melts faster. It is sometimes sold as berry sugar.
I recently bought some demerara sugar which was ground up to caster grade. It worked very well and was delicious in a lemon cake.
You can make your own caster sugar by whirling up granulated in a blender.