I never shot .38 Special cases in my S&W 686 because the chambers would have had to endure the wear of hot gasses in areas where .357 brass would have to fit which seemed to me to be unnecessarily hard on the gun. Also the bullet would have to make a longer jump to the forcing cone which didn't seem the best idea to me for a number of reasons, although none of them would matter in nearly point-blank use.
I used a pretty light load in .357 brass (mid .38 Spl numbers according to the manual with the understanding it would have less bullet energy than the same load in a smaller case) with wadcutters and magnum primers to meet the regulations of my club's indoor range with no ignition difficulties, no FTF's.
It seems to me that downloaded .357's would be less a problem for the gun and especially the cases than excessively hot loaded .38's would be even if magnum primers were used in the .38 cases. I had no convincing evidence that there was any difference in the brass between .38 Special and .357 Magnum so I decided to reload in a manner that it didn't matter if there was any difference or not.
I kept the cartridges in different boxes and never mixed them at any time - the boxes of reloads were labeled appropriately and not next to each other in the ammo locker, and that's as close as they ever got. To be sure I could easily tell which was which I reloaded .357 Mag in some nice .357 nickel-plated cases and used brass cases downloaded for the indoor range. I was happy all round.