There is often confusion regarding these terms.  Full size and half size do not indicate actual paper dimensions.  They are a reference to the original drawing size.  For example, if a drawing file is currently sized at 24″x36″, then a full size print of that file would be 24″x36″.  A half size print, or 50% reduction,  of the same 24″x36″ original would be 12″x18″.  If the original is 36″x48″, then the full size print would be 36″x48″ and the half size print would be 18″x24″.  It all depends on the size of the original.
Since drawings are typically created to scale, full size and half size prints make the most sense when doing calculations or using the drawings for construction. However, if scale isn’t critical, then enlarging or reducing drawing to any standard paper dimension is also possible.