The Beretta Model 38A was an outstanding SMG at the beginning of World War Two, loaded with features and very easy to shoot. However, it was expensive and complex to produce, and pressures of war forced Beretta to progressively simplify its construction. This happened incrementally, but the most obvious set of changes was the adoption of the Model 38/42 pattern. This involved shortening the stock and removing the magazine cover and the barrel shroud. A series of different barrel and bolt assemblies were used, with self-contained springs and fluted barrels at first and smooth barrels with non-captive springs later (as seen on this example).
It should be noted that while the designation 38/43 is sometimes seen referring to this smooth-barrel type, I believe that is not an appropriate name. There is an official 38/43 model; a folding-stock paratrooper pattern (which is exceedingly rare). While it is tempting to assign a specific name to each change in the design, that does not appear to have happened officially with Beretta and these guns.