You're right, that's clearly a refined non-sucrose sugar. But I guess I'm thinking of granulated sugars, i.e. something that differs from white granulated sugar

You're right, that's clearly a refined non-sucrose sugar. But I guess I'm thinking of granulated sugars, i.e. something that differs from white granulated sugar in "only" chemical composition (or as close to that as possible). Otherwise it's not clear to me that the choice is one of sugar molecule or one of other physical characteristics (like moisture content).