Ok, to recap what others have said in this and your other thread, with moon clips there are differences and also there are differences in brass. Most, but certainly not all revolver shooters that use moons and shoot in competitions handload their own ammo. Most of my revo shooting is with a 929 which is of course 9mm so I have to use moons but I also have a 686 6-shot that I had the cylinder cut for moons. I don't use the 686 that much and I don't remember which thickness they are but they are TKs.
I purchased these TKs especially to use with 38 spl. Federal brass. They (TKs) are premium moons (cost a lot) and the brass fits very tight in the moons. Depending on the tool you use (as others have said get the BMT) if the brass isn't correctly seated in the moon clip grove then it will not fit in the cylinder. There are, and this is also an expense worth making, there are gages that mimic the cylinder that you can use to test your loaded moon clips, TK sells them for about $50.00
Getting back to the brass, try another brand of ammo and see if they work with your moon clips better. I know that with 929s some who handload have said that under certain loads the brass expands in the cylinder and is hard to eject. If you check Brian Enos forum you might find something about this but I cannot remember anyone posting issues with 38 spl. One other thing, many commercial ammo makers buy their brass from different suppliers and as long as the brass meets SAAMI specs they use it but there is no guarantee that different lots will have the same dimensions.
TK moons, as mentioned are considered premium, competitors like them and they want tight fitting moons. By this I mean the ammo fits in the clips tightly, not the loaded moon clip fitting in the cylinder tightly. A thinner moon clip might be more user friendly but the rounds will wobble thus in theory causing a slightly longer reload. For my 929 I use inexpensive spring steel moon clips, some I have used soo much and they are worn enough that I can install and remove rounds of ammo without using any tool. These need to be replaces very soon. A few places that sell inexpensive moons are Revolver Supply Store and Ranch Products.
Hang in with moons once you get it you will love them. Also, regarding your 686 grips, exact replacement S&W grips are inexpensive and there are 100s of aftermarket grips available for the L frame. I took a rasp to my stock grips to remove the finger bumps. Very ugly to look at but a huge improvement in shootability. I have a small hand and the groves were in the wrong place for me. You might consider for pin (or steel) shooting Hogue Big Butts. They range in price from about $80.00 to roughly $150.00
BTW and not to change the subject. Even Performance Center revolvers should have action work done on them to lighten and smooth the trigger pull. Right now stock S&W L and N frames have something in the neighborhood of a 14 pound double action pull. Mine have been worked to 7 pounds and I know of some who have even lighter. Problem here is if you go too light you might have to select your ammo for soft primers, I use nothing but federal primers which are considered the softest. You also might want to have the cylinder charge holes chamfered.
