The brass case is only a GASKET, used to seal the firing chamber against the high-pressure gases. The STRENGTH lies in the material and design of the firearm itself. Rimfires are about the only current ammunition where CASE strength is critical to the safe operation of the firearm.
This subject came up on the Cast Boolit site some time back, and at that time I shortened .357 cases of several makes to .38 Special length. Guess what? The shortened .357 brass was almost precisely the same weight as .38 brass from the same maker. This means that there is no practical difference in the amount of actual metal in the .357 cases, as compared to .38 brass of the same headstamp.
Those old Lyman handbooks were NOT giving data for using .38 brass in .357 guns. They were specifically providing heavy .38 loads for use in .38 Special revolvers. I will 'fess up now, and tell y'all that I, myself, personally (not the guy down the street, or a friend of my brother-in-law) used MANY hundreds of "Skeeter" loads (155-grain 358156/ SPECIFIC POWDER LOAD REMOVED BY STAFF ) in a K-frame .38 Special without harm to myself or the gun. Accuracy was superb, extraction was easy, and the gun was still in excellent working order when I sold it.
Would I do that today? No, because I have a goodly number of .357 revolvers, and a limited number of .38 Specials which includes the J-frame 642. I wouldn't want one of the Skeeter loads to find its way into the little gun. However, this discontinuance of heavy-loaded .38s occurred rather recently, when the 642 moved in with us maybe five years ago. It ended about thirty years of successful use of .38 brass in heavy loads, and I'm now using .357 guns for .357 jobs, with .357 brass.
That 358156, incidentally, has two crimp grooves. Used in .357 brass, it's crimped in the front groove. In .38 brass, we have the option of using the rear groove for more case capacity with heavy loads or for use in longer .357 chambers. The front groove can also be used with .38 cases for altering burning characteristics, or normal use in .38 chambers. The bullet is a gas-check design, but I find it works well in many loads without the gas-check attached.
The .38/.357 guns have given me a lot of fun over the years. If faced with that perennial gun-forum question, "If you could only have ONE....", my choice might well fall on the .357.