Yep model numbers are all you need. Your 10 and 15 are K frames. L frames are a small subset: Smith & Wesson L-frame revolvers: models 586 686 386 396 696
Here is a site that will answer most of your questions:
Modern Firearms - S&W ( L ) frame
Here is the text as this is a ru site that some may not be comfortable visiting:
Smith & Wesson L-frame revolvers: models 586 686 386 396 696 (USA)
S&W Model 686 "Distinguished Combat Magnum Stainless" revolver
S&W Model 586 "Distinguished Combat Magnum" revolver
S&W Model 681 - fixed sights variation of the Model 686 revolver
S&W Model 386PD - Airlite Sc 7-shot "Personal Defence" revolver in .357 Magnum
S&W Model 696 - 5-shot revolver in .44 Special
Data for M686 unless noted otherwise
Type: Double Action
Chamber: Models 581, 681, 586, 686, 386 - .357 Magnum; Models 396 and 696 - .44 Special
Weight unloaded: depending on barrel lenght, usually from 980 to 1250 gramm (35 - 44 Oz)
Length: depending on barrel lenght, usually from 190 to 350 mm ( 7 1/2 - 13 13/16 inch)
Barrel length: 63.5, 102, 152, 208 mm (2 1/2, 4, 6, 8 3/16 inches)
Capacity: 6 rounds (7 rounds for M686 Plus and 5 rounds for Models 396 and 696 in .44Spl)
The "L"-frame family of revolvers is one of the youngest and smallest of all S&W families. It was announced in 1980 with four models, all chambered in .357 magnum - 581, 681, 586 and 686. All those revolvers were similar in design, and differed only in materials and sight types: models 581 and 586 were carbon steel, 681 and 686 - stainless steel; models 581 and 681 had fixed rear sights, models 586 and 686 had ajustable sights. The idea behind the whole "L"-frame family was to create revolvers, strong enough to withstand a steady diet of full-power .357 Magnum ammunition while being comfortable to carry for long periods. Basically, these guns were intended as "ideal" service revolvers in 357 magnum. Previous S&W revolvers in .357 Magnum had some drawbacks from that point of view: K-frame revolvers like Model 19 or Model 66 were light but not strong enough for constant usage of powerfull ammunition; N-framed guns, like Model 28 or Model 627 were exceptionally strong, but also too big and heavy. So "L"-framed guns were born as compromise between K and N frames - grip part of the "L" frame is similar to "K" frame, and cylinder part is much stronger, like that of "N" frame.
"L"-framed revolvers quickly became a real sucess, and were adopded and still are used by many police departments across USA. They also became popular across civilian shooters who needed powerful and stong, but moderately sized revolver. Later, S&W developed a set of revolvers in .44 Spl, based on the same frame - models 696 (stainless steel), 296 AirLite Ti (with Bodyguard-like shrouded hammer) and 396 AirLite Sc (Aluminium-Scandium frame, Titanium cylinder). All these guns have 5-shot cylinders and intended for those who wanted to lauch bigger slugs from a relatively compact gun. Latest addition to the "L"-frame family is a model 386 in MountainLite and PD modifications. Model 386 has frame and cylinder dimensions of any other "L"-framed guns, but frame is made from newest lightweight and strong Al-Sc alloy, and cylinder is made from Titanium. Gun is extremely light for such powerful ammo, and has 2 1/2 inch (PD) or 3 inch lightweight (MountainLite) barrels. Another recent addition is a Model 686 Plus, which has seven shot cylinder.
Technically, all "L"-framed revolvers are similar to any other modern S&W revolvers. They have double-action trigger, firing pin is mounted on the hammer. Lockwork featured safety bar, which does not allow to hammer to hit the primer unless the trigger is pressed. Cylinder is locked to the frame by two locks - one at the rear of the cylinder (operated manually by the latch on the left side of the frame), and another on the underbarrel lug (spring-loaded plunger). For loading and ejection cylinder is swung out to the left. Most guns have heavy barrels with solid upper ribs and heavy, full lenght underbarrel lugs. MountainLite guns have lightweight barrels without upper rib and with short underbarrel lug. On most models sights are ramped post front and ajustable rear. Fixed sights models are no longer in production, but S&W Custom shop does small runs of the factory customised M681 revolvers. Cylinder capacity is 6 rounds on most models in .357 Magnum, 7 rounds of .357 in model 686 Plus and 5 rounds if chambered for .44 Special. Some models also may feature factory ported barrels to reduce muzzle jump and felt recoil.
In general, "L"-frame revolvers are excellent combat, self-defence, hunting and sport guns, still wery popular, and not only in USA.