This may be correct or not, but I believe there is/was a difference between the 682 and 682x series regarding frame thickness. I have owned quite a few 686 and 687 guns, but only one 682, which was a 682x trap I bought used several years ago. I purchased a separate single trap barrel for it (I believe from Coles) and fitted it myself, which was a pretty trivial job. It fit perfectly, with the exception of the breech flats being very slightly thicker than the sides of the reciever. I was told when I purchased the barrel that this would be true, as the 682x was built thinner of a slightly higher grade of steel.
I don't know if this is the difference being referred to as the "thick" and "thin" frames, or if that discussion is regarding the regular 682 and not the x series.