A brief overview....
starting with the smallest, J frame is the classic pocket S&W snubbie.. model 36 "chief's special" also models # 31, 34, 37, 60 and countless others. Offered in steel and alloy, and now scandium alloy. Five shots of 38 or now 357 will fit in the cylinder. Or you can get 6 shots of 32 caliber, or 8 shots of 22.
Next is the K frame. This is the classic "modern" S&W frame. Model 10, 12 (alloy), 13 (357, fixed sites), 14 (38, 6" adj sights, target model), 15 (2 or 4", 38 adj sights), 16, 17 (22), 18 , 19 (357, Adjust sites) and some sixty series, I'm sure I'm leaving some out here. This frame was built to hold six shots of 38 caliber. IMHO it is a very elegant frame size, just feels right in say a model 15 or 14. It was streched to accomadate the 357, and model 13 and 19 were born. (More on that later) The original designation for the S&W's in this frame were based on caliber, except the model 1910 Military and Police (which was late just refered to as the model 10). So a 38 would have been a K-38, 22lr was K-22, etc.
L frame is a "larger medium frame". It shares grips with the K frame but it is beefier around the action. Model 586 and 686 are the two most common, I'm sur there's otheres. originally 6 shots of 357/38, now availible in 7 shots. Seems that if you had a 357 K frame, and shot it alot with magnum loads, it would show wear faster than folks liked, so the K frame was born.
N-frame is the Large frame S&W. Classicly the model 25, 27, 28, 29. Six shots of 44mag/44spl, 45colt, 45acp, or 357. .357mag is now availible with 8 shots.
There is also an "X-Frame" built to handle the S&W500 and other really big rounds.
Hope that confuses things...