The Auto Mag's are rimless cases, .357 AM is made from necking a .44 AM case down to .357" so you will never find a case marked .357 AM, there is also a .41 AM.
.44 AM was originally made by two companies, Norma and Aquila of Mexico, Star line makes cases for loading new ammo and you can cut down just about any case with a Mauser/30-06 case head.
The round on the left is a factory Norma .44 AM and the dummy round is a necked down 7.62x51 LC NM case. the .357 AM was a very potent round, I would like to find a 6" S&W Model 27 or 28 and have a unfluted stainless cylinder reamed for it and use full moon clips.
I am working on a 629 reamed for .44 AM and cut for moon clips, maybe some day I will get done.
eQ