S&W Grip Screws
To Ed's excellent response and suggestion I might add a couple of nitpicky additional differences in pre-war grip screws. While the question and Ed's answer were specifically K frame, I think it should be added that there are other differences besides length in S&W grip screws. I admit I haven't made an effort to measure and quantify which grips require exactly which screws, but I do note some additional differences.
There are differences in diameter. The I frame screws are smaller. While K and N frame screws are generally the same diameter, I do find two different diameters among the few spares I have.
There are also differences in how much of the screw shank is threaded. For example, the thread on 1917 grips is distinctly quite short, maybe to minimize wartime machining time.
It can be really frustrating to try to find one with the right thread, thread length, diameter, and length. For me screws have seemed to be hard to come by. I try to think twice before buying grips without screws, and I've learned to double check to be sure the screw is the right one, too, not something else forced into the threads. Jim King