In this condition, I cannot be sure, but it appears that this is a Tri-Jen adaptor cartridge.
These were made by the Tri-Jen Manufacturing Company, 8325 Bererly Boulevard, Los Angeles 48, California, probably during the 1950s and early 1960s. The early production were smooth-bore - that is, the hole through the cartridge was not rifled. Later ones were rifled for better accuracy. They were meant to be loaded with a piece of lead shot, and fired with a normal pistol primer, for short-range, indoor practice. I have the 9 mm adaptor and the .45 auto adaptors in my own collection, both of the rifled type. I don’t collect revolver, and could be wrong on the exact ID of this item, as I am not that familiar with the shape of the .38 round. However, the Tri-Jens were blackened steel, and the base of your round is pretty much identical in appearance, except for the wider surface due to the cartridge rim, as my 9 mm rounds.
They were boxed 6 adaptors to a box, with a small steel rod for seating a piece of shot, and knocking out a fired primer, as well as a small quantity of lead shot of the correct diameter.
The only thing that puzzles me is the diameter of the hole (bore) of your round. I would think they would all be the same, but the 9 mm measures 0.152" bore diameter at the nose, and the primer pocket, while the same
width as you show,0.209", is 0.1205" deep, not 0.147" as you indicate yours is. One of the lead shot that came in the box with my 9 mm unit measures 0.1495" in diameter, Considering the rifling, that would probably be quite compatible with the 0.152" bore.
The bore and primer pocket differences could indicate that your .38 adaptor is made by someone other than Tri-Jen. The depth of the primer pocket of yours seems uncompatible with a standard primer, though.