The M4 was a welded hull vs. the M4A1s which were cast hulls.
the Authentic kit by MP Models allowed you to build an M4 or early M4A3 Ford. It was a conversion for the Tamiya M4A3 kit or Italeri M4A1 -- this was before the Tamiya M4 Early Prod kit was made.
The problem with the base Italeri M32 kit is that it sought to depict an M32B1 using the hull from their M4A1 76W kit. The issue is that all photographed M32B1s are made with the small hatch M4A1 hull (such as the new Tasca M4A1 hull or the older DML 6048 kit). I'm not aware of any extant photos that use the combination that Italeri offered.
By using the Authenti kit M4, Gary makes the M32 in a correct configuration. (one could also use the M32 parts and place them directly onto the Tamiya M4 kit). There were also M32B2s and M32B3s (using the M4A2 and M4A3 respectively)
HTH