The word "Heavy" was first applied to the wider rib weight matched K38 and K32 Masterpiece revolvers, their ribs were widened to bring their barrel weight closer to the K22 which weighed more due to its smaller bore.
The .44 Magnum and Combat Magnum are a different story, both appear around 1955 and were introduced with wide rib barrels and shrouded ejector rods to add weight and help tame recoil,
Since there were no lighter barrel versions preceding them there was no need to apply the "Heavy Barrel" moniker.
The Model 10, 14, 64, 36 etc had lighter barrel versions that either preceded them or were offered simultaneously, the Heavy barrel term made sure you were getting the right version if you ordered one or 100 from the factory. Btw the frames are usually finished differently at the top where they meet the barrel so putting a HB on a frame originally used for a tapered barrel will thread in but won't look right cosmetically.
Years later lighter tapered narrow rib 29/629 686, etc were introduced and called "Mountain gun" to distinguish from previous heavier wide rib versions.
S&W kinda made up the rules and broke them as they went along but there is a sorta logic to it if you follow their Model line through its evolutionary changes from 1930 to today.