Barrel assemblies for the 357 magnum will NOT work on the model 40 357 supermag. The barrels will, but the shrouds will not. That being said, if you have a barrel assembly from another supermag, you can use a 357 mag barrel and the other supermag shroud. (example: 357 mag barrel and a 445 supermag shroud.)
Here is some general interchangability info:
All supermag shrouds are the same, just different markings.
All large frame shrouds are the same, just different markings (44 mag, 41, 45LC)
All small frame shrouds are the same, just different markings (22, 32, 357 mag, ect.)
Supermag shrouds CAN be used on large frames (ex: 445 supermag barrel assembly on a 44 mag.)
Large shrouds CANNOT be used on Supermags (the slot in the shroud for the ejector rod is too short.)
There are only 2 different barrel nut sizes small & large/supermag. They are not caliber specific.
Frames are threaded differently according to caliber. So you cannot for example screw a 22LR barrel into a 357 mag frame.
As I stated above for the 357, barrels are caliber specific & will screw into any frame for that caliber. (44 mag works also in 445 supermag, ect.)