The .38 AMU wasn't rimless. It uses the same "rim" as the .38 Super, which is semi-rimed. The bullets were HBWC, seated flush with the case mouth. This was done for two reasons, which RC touched on. The first was the magazines wouldn't hold anything longer, and the second was the HBWC bullet is the most accurate for bullseye shooting, which is what those guns, and the S&W Model 52, were specifically made for.
Remington and Federal both made .38 AMU ammunition, and I'm not sure about Winchester. All the .38 AMU brass I had was either Remington or Federal. The Remington brass was in boxes marked ".38 AMU" in regular factory printing, but the Federal brass was in .38 Special wadcutter boxes, with printed labels added over the factory .38 Special printing on the boxes. There was also a rubber stamp of ".38 AMU" on a couple of places on the Federal boxes, probably so the GI's wouldn't get them mixed up with regular .38 Special ammunition. The labels and stampings appeared to have been done at the factory.
I gave the Federal brass I had to the Federal reps at the SHOT Show a couple of years ago, and the Remington brass was given to the Remington reps at the same show. They promised me it would go in their company displays, but I have my doubts it ever made it there.........
Hope this helps.
Fred