OK. J-frame traditionally meant 5-shot 38Spl, more recently 5-shot 357, plus a lot were set up as six-shot .32 or up to 9-shot 22LR or 8-shot 22Magnum. Most shipped with 2" barrels.
K-frame was originally a six-shot 38Spl, later upgraded to a somewhat strength-marginal 357. Also shipped in .22 and the occasional oddity.
L-frame was meant as a tougher 357 than the K-frame, originally six-shot, later seven-shot.
N-frame was originally 44Spl, some shipped in 45LC or 45ACP, then the very first 357 shipped with it. It was then the platform for the 44Mag. Most recent setup is 8-shot 357.
X-Frame is the newest, for the 500S&WMagnum.
Now. If anything else from another vendor is able to eat from a speedloader similar to one of the above, we'll sometimes call it a "whatever-class". Taurus has a habit of very closely copying S&W sizes. Ruger often varies in terms of heft, but will often take the same speedloaders as an S&W. So the SP101 eats from J-frame speedloaders, the Redhawk and SuperRedhawk eat from N-frame loaders and I seem to recall the GP100 is more or less L-frame although not quite perfect. And the out-of-production Service/Security/Speed Six series were "k-class" (although a bit tougher).
And so on. Basically, the S&W sizes are a good starting point for judging anything else, while speedloader compatibility is an objective standard of comparison.