What is the difference between a shell element and a 2D solid element in ABAQUS?

The 2D Planar elements (For example : CPE4, CPE8 - plane strain analysis and CP4, CPS8 - plane stress analysis) are only used in situations where the loading is confined to the plane of the elements. The elements only have planar variables (d.o.f) ux, uy. This means that there is no variation in the Z direction. 
Shell elements are needed for out-of-plane loading. Consider a square plate subjected to a loading normal to the plane of the plate. This requires shell elements and use of plane stress/plane strain type of elements would be inappropriate under these circumstances. 

Shell elements can also be used where the loading is planar but the material is made of composites. Since shell elements by definition allow for through thickness variation of material properties these are the appropriate elements to be used in these cases.