Lead and powder buildup in the cylinder. You didn't clean it very well. Get a brass brush and go to it. There's nothing wrong with the gun.
That is a very tough revolver(pistol is usually a reference to an autoloader)that is not at all ruined. As many have told you already, the chambers are fouled from the .38 SPL you shot in it first. It is very important to clean your chambers after shooting the shorter ammo before firing the .357 MAG ammo, as high pressure could result from the crud squeezing down on the case mouth holding the projectile too tightly. In the .454 Casull revolvers by Freedom Arms it is imperative to clean the chambers after using .45 Colt ammo before firing the full length .454 ammo through the gun. Even their fine and very strong revolvers could blow up if misused like that.
Thank you all for your helpful replies.
If regular brass brushes don't get it, try a Lewis (spelling?) Lead Remover. They are patches of brass screen that are forced down around a rubber mandrel. If there is still fouling this will get it.
If you want to continue to shoot lower powered rounds, save your .357 brass and handload them with a lighter load. Use a reputable reloading guide for a good recipe.
You have fouling as others have said.
You don't need a brass brush or a Lewis Lead Remover.
Cut about a 1" square from a new piece of Scotch-Brite (the green scratch pads sold in the Supermarket for scrubbing out pots & pans). Use this to clean the chambers by pushing it through with your cleaning rod. Solvent is a help here.
Next time, inspect the chambers and the bore by looking through them at a light or at a piece of paper held to catch the light. You will see whatever crud has been left behind by ineffective cleaning.
Many have given you the answer before me. Shoot the 3.57 mag rounds first, then switch over to the .38's. The powder residue will most definitely cause this.
As also noted, before shooting the 3.57 and after .38's, running a bore brush though the cylinder is an option as is a boresnake.
I used to have a 686 and shot lots of cheap 38 special rounds through it and never encountered this problem. Of course I was a fanatic about cleaning and would often stop and wipe the gun down during target practice. I found doing that gave me time to think about my target shooting.