Hammer profile is the easiest way to distinguish the two actions. Hammers on the short throw guns have a deeper scoop on top of the hammer spurs, giving the impression that the spur springs from a little lower on the hammer body. The long throw actions have hammers with a shallower scoop. Compare the following two hammer profiles.
This is a long throw M&P from early 1947.
This is a short-action K-38 Masterpiece from early 1948:
The deeper scoop in the hammer of the short action gun is characteristic of the so-falled "speed" hammers seen in the short-action postwar Masterpiece revolvers. S&W actually mentioned the new "high-speed" hammer on the gold picture boxes in which they shipped the new short action guns.
The company made the argument that the shorter hammer throw made for a faster lock time and, in consequence, better accuracy because there was less opportunity for barrel wobble while the hammer was falling.
Ignoring the scant production of barely 1000 short-action K-22s in 1940, all short action production postdates WWII. The modern K-22 Masterpiece (K-22 Third Model) was the first postwar gun that featured the short action, and those began to be produced in 1947. The fixed sight K-frame .38 M&P models continued to be made after WWII until serial number S990000 (round number), at which point the last 10,000 M&Ps were produced with the short action. All C-prefix M&Ps are short action revolvers. That change came in April of 1948, which is also close to the time the adjustable sight K-38 Masterpiece began to be produced in volume. The K-32 Masterpiece began to ship in volume in early 1949, and those were all short action revolvers as well.
In the N-frames, the long-throw actions continued to be produced through 1949 and into early 1950, and then the new Model of 1950 N-frames introduced the short action. All Model of 1950 N-frames incorporate a short action.
I'm a big fan of the long action guns because, as a class, the actions just feel smoother to me. But that doesn't mean short actions can be condemned as stiff or rough. Some of my short-action revolvers have enviably smooth actions, though others of them are not as smooth as most of the long action guns that I like. You'll hear assertions that one action is better than the other for a variety of reasons, but I'm not sure I think the generalizations mean much. The question is whether the action in a single gun is satisfactory by itself, and both long action and short action guns can be tuned to silky precision.
ADDENDUM: Hmm, slow to the party, I see. While I was writing this War and Peace-length response, good answers were provided by others. I'll leave this post here because I think the photos show a quick way to make the distinction.