The -01 and -02 come with a PCB for the microswitches and use a 5-pin connector for fast and easy replacement in arcades. The LS-32 comes with regular microswitches.
-01 PCB:

And yes, the LS-32 comes with the flat RE plates and the 32-01 comes with the "S-shaped" SS plates. IIRC, the 32-02 comes with the -01 PCB and the RE plate?