If an extrusion is converted to a surface or polysurface, the resulting shape is exactly the same.
Extrusions can be converted to surfaces or polysurfaces using ConvertExtrusion or Explode. ConvertExtrusion results in a surface or a single polysurface, and has the option of also retaining the original extrusion. Explode replaces the original extrusion with a surface or surfaces. The user needs to Join the surfaces if a single polysurface is desired.
The only significant advantage using extrusions offers is the amount of storage needed by extrusion objects is less. This is because the method of representing extrusion objects relies on the shape characteristics of extrusions. Note that the results of some “extrude” commands cannot be stored as extrusions and must be surfaces or polysurfaces.
The reason to use extrusions is if your model has many objects which can be represented as extrusions and the resulting reduction in required storage is important to you. The UseExtrusions command allows selection of extrusions to be used where possible or to always use surfaces/polysurfaces.
From Lightweight Extrusion Objects [McNeel Wiki] which @Rodri linked to above.
Customers were creating architectural models with tens of thousands of objects that were simple extrusions. When traditional polysurfaces were used to represent the objects, the models were sluggish and used lots of memory resources. When these models use the lightweight extrusions, the models were responsive and there was plenty of memory available.
A “solid” in Rhino is simply a closed surface orpolysurface. The user doesn’t make a choice between a “solid” and a closed surface or polysurface. If a closed surface or polysurface is created Rhino treats it as solid. If the surface or polysurface is modified so that it is no longer closed then Rhino stops treating it as solid.