Yes, the L frame is slightly larger than a K frame, so the cylinder is slightly larger.
There is a heck of a lot more to it than what you have quoted on the S&W website.
Let's go through a little bit of history.
Going back to 1896, the first revolver Smith and Wesson made with a swing out style cylinder was chambered for the 32 S&W Long cartridge. It was called the 32 Hand Ejector, 1st Model. Hand Ejector refers to the fact that unlike with the older Top Break revolvers, which automatically ejected empty cartridges when opened, with the new revolvers empties were not ejected automatically. Instead empties had to be ejected 'by hand' by pushing in the ejector rod after the cylinder was opened.
This revolver was a six shot revolver. It was the perfect size for a six shot 32 caliber revolver. It was built on what came to be known as the I frame.
In 1899 Smith and Wesson developed the 38 Special cartridge, and a new revolver was introduced to chamber the 38 Special. The new revolver was larger than the I frame, it was the perfect size for a six shot 38 caliber revolver. The new revolver was called the 38 Military and Police, or the Model of 1899 Army-Navy revolver. The frame it was built on became known as the K frame.
In 1908, S&W introduced the 44 Special cartridge, and a new revolver was introduced to chamber it. Bigger again than the K frame, the new revolver was built on the N frame. The first of these was the 44 Hand Ejector, 1st Model, also known as the Triple Lock because of the unusual 3rd latch that secured the front of the cylinder yoke to the barrel.
For a long time, the N frame was the largest revolver S&W made. The 3rd latch was discontinued in 1915, but N frame revolvers were chambered for a variety of cartridges. Two of these were known as the 38/44 Heavy Duty and 38/44 Outdoorsman. These were chambered for 38 Special, but were created specifically for a high velocity 38 Special cartridge. The N frame was chosen for these revolvers because the larger cylinder would have more metal between the chambers than a K frame cylinder. This was necessary at the time to contain the high pressure developed by the high velocity 38 Special cartridges.
This is a 38/44 Outdoorsman. The 38/44 Heavy Duty was the same except it had fixed sights rather than adjustable sights.
S&W was concerned the high velocity 38 Special cartridges might be loaded into a K frame revolver, which might not be able to handle the higher pressure of the high velocity cartridges. So in 1935 S&W lengthened the cartridge case about 1/10" and called the cartridge the 357 Magnum. The new revolver, also built on the N frame had longer chambers to accommodate the longer shells. The new revolver was simply called The 357 Magnum. The early ones were the Registered Magnums, part of a program of customized 357 Magnum revolvers that S&W built to the customer's specifications, and registered the revolver to the owners.
Later, in 1957, when S&W went to a numbering system for naming their revolvers, The 357 Magnum became the Model 27.
The N frame 357 Magnum revolvers were big and heavy. Because the bore and chambers were smaller than the 44 and 45 caliber N frames, they 357s were heavier than 44 or 45 caliber N frame of the same barrel length.
By 1955 S&W felt that metallurgy had improved enough to offer a 357 Magnum revolver built on the K frame. The new revolver was called the 357 Combat Magnum. After 1957 it was known as the Model 19.
Since the early days of the K frames revolvers, a flat had been cut onto the bottom of the forcing cone. This was a clearance cut put there to clear the gas collar on the cylinder. Never a problem with 38 Special revolvers, but sometimes with the new K frame 357 Magnums the thinner cross section at the bottom of the forcing cone could split from high velocity 357 Magnum ammunition. The arrow is showing the flat spot on the bottom of a Model 19-3.
That is why the L frame revolvers were developed. The cylinders were slightly larger in diameter than a K frame cylinder, not as big as a N frame cylinder. The larger cylinder meant there was no need for a clearance cut at the bottom of the forcing cone. This is a photo of a L frame Model 686 forcing cone. Note there is no flat on the underside of the forcing cone.
That is what S&W is talking about when they say the L frame is built for continuous Magnum usage. Just to be clear, there was never a clearance cut on the bottom of a N frame revolver, and a N frame 357 Magnum revolver is also perfectly suited for continuous Magnum usage. But some shooters think a N frame revolver is just too big and heavy.
This is the forcing cone on a N frame, 357 Magnum Model 28. No flat on the bottom. Notice how massive the barrel is.
Regarding J frame 357 Magnums: The J frame is the descendant of the old I frame. Pretty much the same size, just a bit different in shape. Personally, I have no use for a J frame 357 Magnum. 38 Special, yes, but I don't like holding onto a J frame when firing 357 Magnum cartridges, too much recoil for my dainty hands.
Here is a photo showing the chambers of a K frame 38 Special on the left, and a L frame 357 Magnum on the right. Note that because the cylinder is larger in diameter, there is room to stuff in an extra chamber into the L frame cylinder.
Here is a photo comparing the different frame sizes of Smith and Wesson revolvers. Starting at the upper right, N frame Triple Lock. Next down a K frame 38 Special. Next down a J frame Model 36 (38 Special). Upper left an I frame 38 Regulation Police, and finally a tiny M frame Lady Smith.
I did not own a L frame revolver when I took that photo. Top to bottom in this photo is a K frame Model 19-3, L frame Model 686 and a N frame Model 28.