Just to add to the confusion (but perhaps shed some light!), the three primary action types, Sidelock, Boxlock, and Round/Trigger Plate, can all be "rounded" (really wish Dickson and/or MacNaughton had picked a more definitive name). Seems most of the early back action Black Powder rifles were rounded on the bottom. This made them trimmmer and more comfortable to carry in one hand. Although early rounded hammerless sidelocks are sometimes seen, the majority of them were more squared on the "bellies". It appears that the boxlocks were less rounded from the beginning perhaps to save labor time/costs. The Scottish trigger plate actions seem to have been rounded from the first. Perhaps because the Highlanders were carrying their rifles more during their stalks through the hills and wanted a more comfortable rifle to carry with one hand? Exceptions existed (some of my favorite BLs are the early rounded Westley DLs), but I believe that is pretty much on track for the historical part.
The new H&H "Round Action" (I really, REALLY wish Holland's had picked ANY other name- What's so wrong with, "New Dominion"??) is a SL which is rounded, both on the action bottom and through the head and wrist of the stock. These were cost saving measures as there is less hand work to fit up an action and stock made as such. What I learned in Vegas is the rifles have a through-bolt running through the stock to reinforce the stock and action. I can see where that is less expensive (and far less expensive than the extended top tang and the full bottom tang of a Royal!) but it should be plenty strong and conceivably make a more rigid and thus more accurate stock to action mating.
I like the new Holland Round Action (not as much as the older unbolstered Royals, though!) and would probably order one if the D%*# dollar wasn't so d*^@ weak! Of course that sparse and course engraving would have to upgraded to something more palatable.
Whew! This post should upgrade me to at least 250 Rook status!!!