I recently picked up this box which contained about 20 rounds having the belted bullet shown below. Both the box, though difficult to see, and a U.M.C. lithograph (known to contain inaccuracies) illustrate this round with a bullet showing a groove at the case mouth like the 32 or 38 M. H. & Co. I also have one round with that bullet. Of course none are headstamped. The belted bullet round has a case with a beveled rim while the grooved round has a case with a rounded rim. Both are the shorter .88ʺ case length versus the 32 S&W Long .92ʺ case length. I
IAA JOURNAL #384 has an article on the 32 H&R Long. I’m not sure it answers any of your questions.
Great box. The .32 Harrington & Richardson cartridge is the same as the .32 Merwin & Hulbert; you’ll note on the side of the that the cartridges are ‘Adapted to Harrington & Richardson and M.H. & Co’s Double Action revolvers’. I believe the rounded rim cartridges are UMC made and are original to the box. These 88 grain bullets are lighter than the .32 S&W long bullet, but they look very similar. Its hard to say who made the bevelled rim cartridge, as a number of copmpanies used this style rim at some point in their production, including UMC.