When you look through the view finder, the array of focus points is a matrix of small squares. But each of those small squares also has an even smaller square in the center of it. When using Single Point AF, you are using the larger, outer square for that point. When using Single Point Spot AF, you are using the tiny square in the center of each focus point.
Just to be clear, with Spot AF the actual AF point is still slightly larger than outer square. The area being used for AF isn't nearly as small as the little inner box, that 'double' box is just the indication that Spot AF is being used.