.38 Short Colt is an obsolete, early cartridge with a heeled bullet (a smaller section that fits inside the case, like a 22 rimfire). At one time, they were quite available and probably cheap. They are no longer either. They were used in revolvers, I know of no semi-automatic in which they would shoot. From the photos, I have no idea what arm would be the larger gun.
I do know the U. S. military has (or had) such an adapter as a the 'primer' for cannon rounds. Except the 'smaller' round was a blank .38 Special made to set off the cannon round (155mm towed howitzer). Don't know what earlier ones might have been.
The outer section looks like a chamber adapter, to fire the (presumably cheaper and less recoiling round) in a larger arm in place of the more expensive and harsh recoiling round. However to be effective in such manner, the 'larger' arm would have to be functionally the same bore diameter as the smaller round (I believe one can still get an adapter to fire .32 ACP ammunition in a .30-06 rifle; at one time they were plentiful).
Likely these were thrown away in the belief they were worthless, the cartridge and arm for which they were made no longer popular or in use. But a collector of the old gun in question might be interested from a collector standpoint. Or a cartridge collector.