Different frame? K frame is a k frame. The 66 has a standard barrel, adjustable sights, and of course a slightly longer cylinder to accept the 357 round.
There was a short run of 64's in 357, as there was a run of 10's in 357 for the NY Troopers. I am sure the 64 could handle a 357. Since S&w is still making 64's, I don't know why they don't make them in 357. T..........
All K frames are not the same.
There are round butt and square butt frames,
Stainless steel, Carbon steel and aluminum frames,
Long and short action 5 screw, 4 screw, 3 screw frames,
Smooth tang, 6 groove tang and 10 groove tang frames, Pre and post barrel set pin frames,
Pre IL and Post IL , new and old cylinder stop frames,
Center fire frame mounted firing pin and non frame mounted firing pin frames,
Old style rear site cut and new style rear site ( rounded rear site pre drilled for scope mount) frames,
K Target rimfire frames for non rib barrels (pre war),
K Target rimfire frames for narrow rib barrels,
K Target rimfire frames for wide rib barrels,
K Target rimfire frames for full underlug barrels ,
K rimfire fixed site frames,
K Target center fire frames for non rib barrels (pre war),
K Target center fire frames for narrow rib barrels,
K Target center fire frames for wide rib barrels,
K Target center fire frames for wide rib ejector rod shroud barrels,
K centerfire fixed site frames for wide rib barrels,
K centerfire fixed site frames for narrow "Pencil" barrels,
K centerfire fixed site frames for non ejector rod shroud barrels,
K centerfire fixed site frames for use with ejector rod shroud barrels ,
K Target Magnum frames ,
K Magnum fixed site frames for use with shrouded ejector rod barrels,
K Magnum fixed site frames for use with non shrouded ejector rod barrels ,
The SB 2" Model 15 snub frame is unique to that model ,
The 2.5" RB snub Model 66 and 19 Magnum frames are unique to those models,
The Air Force KTX38 Model 56 frame is unique to that Model,
The PC Model 17-8 Heritage rimfire frame is unique to that model,
Lastly cant remember if the Model 53 Jet and Model 547 frames are different but they might also be unique to those models.
The Model 64's and 10's made in .357 pre date the Model 13 and 65 introduction but those had to receive the Magnum heat treating to add strength, (They didnt just drop a 357 cylinder in a run of the mill Model 64 or 10 frame.).