The following is copied from Sage's website (which is where I usually purchase gas checks for personal use):
To add to the confusion, the names of the checks have changed over the years. Here is a package of checks that I received directly from Bullet Swaging Supply years ago, labeled "40-41 BSS". They take a 0.380" shank and have a 0.417" O.D., so they are equivalent to what Sage calls a "41 BSS." But my design program lists them as a "40 Gator," because they are what I recommend for 40 caliber bullets. They will also work satisfactorily for 41 magnum (0.410" - 0.412") bullets, hence the label "40-41," though if I were casting for 41 magnum I would prefer a mold cut for the Hornady 416 check, just because the Hornady is a more common check and you can count on Hornady to be around for many years to come.Please Note: There are different gas checks for the .41 caliber molds and one especially for .40 caliber molds.
#1 .41 Lyman - the shank size is .397.
#2 .416 Rifle - the shank size is .393.
#3 .41 BSS - the shank size is .381.
#4 .40 BSS is a gas check especially made for .368 shank 40 caliber NOE bullet mold.
General Rules Of Thumb For Choosing A Gas Check:
-- pay attention to the shank diameter and match it to the check.
-- you want the O.D. of the check to be 0.003" - 0.005" larger than the size-to diameter so that the check will "crimp" on when sized. If it doesn't crimp on, it's not the end of the world, and will probably still shoot OK, but don't blame the mold maker if the resulting fit is a little loose.
-- if the O.D. is too big and if your sizing die sucks (and most mass produced sizing dies do suck) then the sizing die may mangle the check. However, there is a simple solution -- fix the sucky sizing die by chamfering the opening, then oversize checks will work fine.
On my part, I will update my 40 / 41 check names to agree with Sage's website. Also, if you ever want a mold cut for a particular check that is not listed on the design program, I am usually willing to do that providing 1) you send me a half dozen sample checks and 2) the check O.D. is big enough to crimp on when sized. I don't like to cut molds for checks that won't crimp on because then I get blamed for the resulting loose fit.