I still don't understand the differences in the frames.
Oh, sorry, didn't answer that, and it doesn't look like anyone else did.
The K frame was invented as a 38 call frame about 1898. It has proven one of the best and I believe the most popular revolver design ever, with many, many millions of guns made since then. In the '50s, to satisfy LE demands, the cylinders were given new steel and heat treatment to make them safe to use the 357 round, and to create a duty 357 that was cheaper than the 27 and easier to carry all day than the bulkier/heavier 28 (same size as the fancier 27). A classic was born in the "Combat Magnum" - aka model 19. The 66 was introduced in 1971 or 72 I believe as the stainless steel version of the 19.
In the 70s, two things happened in the marketplace - 1) Colt's Python, on a frame size between the "K" sized 19/66 and the "N" sized 27/28, started making big inroads in the marketplace for 357s, which S&W had owned since it invented the cartridge/platform in 1935. 2) A now-defunct ammunition company, Super-Vel, introduced some screaming hot 125gr. high-velocity loads, that cracked the forcing cone on some K frame 357s, usually in repeated long strings of fire at the range. The gun was not designed for this hyper-sonic light load, and it got an undeserved reputation based on this one marginal type of ammunition. The ammunition itself was discontinued as unsuitable, but the damage to the reputation of the K frame 357 was already done.
S&W needed to innovate to beat the Python, so they created the "L" frame, which is a frame tailored to maximize the .357. It is roughly equal in size to the Python. It is about 1/8" wider in the cylinder than the K, and about 3/16" taller in the frame, and slightly longer in the frame. It carries more easily than an N, and only a bit heavier and bulkier than the K. It came out in 1980 to replace the 19/66 as a LE sidearm. A love/hate feature of it is the full-lug barrel - which aids greatly in taming recoil, but also makes the gun heavier to carry and point, and slower to acquire multiple targets.
Normally I would recommend someone who wants a general-duty 4" revolver to consider the 686. It is usually cheaper and easier to find than a nice 66. But if you are already looking at a nice one for $400, I'd say grab that. You can always trade someone a nice 66 for a 686 should you later change your mind. You can't usually persuade a 66 owner to part with his gun in trade for a 686. That should say something.
Here are comparative pics of a 2.5" 19 K frame (same as a 66, just blue), a 4" 686 L frame, and a 3.5" 27 N frame.