Design Layers are one of the fundamental organizing concepts in Vectorworks, They are used to break the design into manageable chunks, but they should not be confused with Classes. Design Layers as well as Classes are used to create the structure of a file, these then enable the creation of drawing sets using Viewports and Sheet Layers.
On the other hand, Levels and Stories are not used to help create the drawings – they are used in building projects to control the elevation of components. So where the Design Layer might be the foundations, the Levels might control the bottom of the footing, the top of the footing, the underside of the slab, or even the bottom of the cladding. Accurate control of these Levels will dramatically improve your Building Information Modeling (BIM) with Vectorworks.
While Design Layers are like containers (they store all the information related to this layer), Classes are an attribute (assigned to an object to control its graphic style or visibility), Levels and Stories are used to control the 3D elevation of the building elements.