These definitions are common and as old as the levergun itself. Unfortunately manufacturers like Marlin and Henry cater to the modern shooter who really doesn't care too much about history or such minor details.
The assertion was that “…Winchester, Marlin and a whole slew of others.” adhered to the convention and definitions. Apparently Winchester does, but it doesn’t appear that Marlin does, and I couldn’t find any others that did (other than companies making replicas of Winchester vintage lever actions who adhered to Winchester’s convention), let alone a slew of them.
The crescent buttplate was commonly referred to as the "rifle" buttplate. The carbine and shotgun buttplates, the same way. These were specific "rifle" and "carbine" features. Kind of an important distinction when you have an overlap of barrel lengths. Of course, back then you could special order a rifle with whatever features you wanted and there are some in existence that mixed rifle, carbine and shotgun features.
I see that Winchester does appear to name their products along those lines—is that the background for the assertion? If so, it might be reasonable to make the point that Winchester defines carbines and rifles a certain way, but going farther and asserting that it’s a widespread convention that applies across the board and to any lever action firearms, antique or modern, made by any manufacturer would be much harder to justify.
For example, Winchester also made some of their leverguns in what they called a “musket” configuration, but I’ve not seen any claims or evidence that their product naming convention officially redefined the term “musket” (which like the term 'carbine' existed before Winchester began selling firearms) or even that it established an official definition for that term that applies to all lever action rifles.
Furthermore, crescent buttplates are pretty uncommon these days on any firearms and heavy or octagon/half-octagon barrels aren't exactly prevalent on modern leverguns which brings up the issue that if this convention is still in place across the board, there would be almost no official lever-action rifles being made today. They are, if one chooses to follow Winchester's convention, carbine/rifle hybrids.
None of this stuff was random or arbitrary, it all had purpose. The rifle butt takes more time to get settled. The carbine but was faster into action. These were the assault rifles or sub-machine guns of their day. Meant for fast handling, short to intermediate range (all relative) and hard use, usually on horseback. They were also more utilitarian in nature.
The intended usage all makes perfect sense, but it really doesn’t establish the idea that those features are universally accepted to be the definitive distinctions between lever-action carbines and rifles.
People seem to have blinders on and only focus on the barrel length to distinguish rifles from carbines.
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I don't know why this is such a foreign concept to some folks, they did the same thing with the M16. Is the barrel length the only thing that distinguishes the M16 from the M4? Nope. We still refer to the buttstock and buffer system, as well as the gas system and handguard configurations as distinctly "rifle" and "carbine". The shorter, adjustable butt has at least as much to do with fast handling as the shorter barrel.
I don’t think that anyone is saying that the only way to make a carbine is to shorten only the barrel. It’s quite often true that a “carbine” by the commonly accepted general definition, is designed to be more compact/light in more ways than just a shorter the barrel, but it’s also sometimes true that a “carbine” differs from the rifle it was derived from only in terms of barrel length and any modifications required to accommodate the shorter barrel. And Marlin & Henry also use the term “carbine” to refer to pistol caliber leverguns that have lengths and external appearances that are essentially identical to their “rifle” offerings.
As far as the M16/M4 differences go, I’m not sure that they are especially relevant to the assertion which was apparently intended to be very specifically about leverguns. i.e. “The action absolutely matters. These are important distinctions that apply to leverguns.” I was specifically asking about where these leverguns definitions exist other than perhaps as inferred from Winchester’s product naming convention. I think we can all agree that if conventions about barrel bands, saddle rings, octagon/half-octagon, fore-end caps, crescent buttplates, etc. do exist, they are very unlikely to apply to long guns in general, given that such combinations of features are quite uncommon on other action types.
Finally, not to put too fine a point on it, but the reference that started all this was to a Marlin 1894CSS not to the 1894C Cowboy. As far as I can tell the 1894CSS (not currently stocked by Marlin) had a barrel band, round barrel and non-crescent buttplate, so even if Marlin did adhere to Winchester’s convention (and it appears they do not) it would be closer to fitting Winchester’s idea of a lever action carbine than Winchester’s idea of a lever action rifle, even without a saddle ring. So the original comment about the rifle being a carbine was accurate by not only Marlin's standards, but also apparently by Winchester's.