I ended up with these 6 rounds of Peters .38ACP ammunition.
The bullets look like they are steel-jacketed, but they do not attract a magnet. They appear to be copper-jacketed bullets with either zinc or tin plating over the copper jacket. I’m pretty sure that the silver color is a plating/coating. There is evidence in a few spots where the silver-colored plating has worn off/oxidized away that what’s underneath is some kind of copper or gilding metal. You can see one such spot in the top round in the picture.
The headstamp is PETERS .38 A.C.P. The cases have a well-defined smooth cannelure.
I would be interested to know when these were made although that might be a tall order. Peters was bought out by Remington in the mid 1930s, but they continued to use the name for some time. However, the .38ACP wasn’t a common round–maybe that combined with the headstamp (or other information from the appearance of the rounds) might provide some clues.
The rounds were probably originally owned by a person who passed away in the 1960s.
These 6 loose rounds were included in a package deal along with a full box of Remington conventional copper jacketed .38ACP ammo. The Remington ammo was made in 1961 or 62, based on the printing pattern on the box. I have some reason to believe that the loose rounds could be a lot older than that but no way to prove it.