The 66 is a slightly less robust revolver than the 686 - that's about the sum of it.
The Model 19 - and later its stainless brother, the 66 - were introduced at the urging of Bill Jordan back in the 1950's, IIRC. He wanted the power of the .357 Magnum cartridge - until that time, available only in the very large N-frame revolvers - to be offered for police use in the much smaller and lighter K-frame size, which until then had been used only for cartridges up to .38 Special (e.g. the Military & Police, later evolved into the Model 10). S&W were dubious, but did a bunch of testing with stronger steels, etc., and eventually got it right.
In later years, with the development of hotter .357 Magnum loads like the 125gr. JHP at over 1,400 fps, the K-frame .357's began to show accelerated wear and tear. The frames showed "flame-cutting" above the forcing cone, and the guns would "shoot loose". In order to eliminate these problems, S&W introduced the L-frame 581/586 and their stainless-steel cousins, the 681/686. These have the same grip size as the K-frame, but a thicker steel topstrap and more robust internals, to handle the repeated firing of the hotter loads. (Ruger, BTW, did much the same thing, introducing the GP100 as a tougher gun than the earlier and smaller Security-Six. However, S&W kept the 66 in production, adding the 686 as a tougher high-end option, whereas Ruger actually stopped producing the Security-Six - a bad decision, IMHO.)
I have both 66's and 686's. For practice, I largely stay with .38 Special loads in the 66. With the 686, being tougher, I'm more comfortable practicing with full-house magnum loads. For carry, I keep a couple of 2½" 66's, which conceal easily and are very handy. For larger revolvers, I prefer the tougher 686.
Hope this clarifies things.
