Is it the sticker on the air cleaner????
Too much gray to make this much of anything beyond opinion. Add that I think the factory played the "HP" card too loosely and it isn't much more than a marketing label.
But a fun discussion regardless.
My opinion is that anything that has upgrades to add horsepower beyond what is necessary makes it worthy of the HP stamp. It also means that doing things like adding more carb (1bbl -> 2bbl) doesn't necessarily mean "HP" if the intent was efficiency and not performance (e.g. Super Six). Was it designed to be faster or did it get faster because it was designed to be more efficient?
I would lump the 383 4 bbl with the standard cam in the non-HP listings. And anything else the factory put a 4 bbl on but didn't do anything else to. I would also lump the 5.7 G3 in the non-HP category.
383 with the 440 cam? 360 with 340 heads/intake/exhaust? Absolutely HP. Even the 318 Police special (IMO) is worthy of the label even if the results weren't exactly spectacular as it's what they had to work with. 426 G2? 6.4/6.2 G3? 440 SixPack? I can't imagine anyone would argue with those.
I think this applies holistically to the vehicle as well. In some cases the motor wasn't really messed with, but by offering it in a vehicle you couldn't get it in before and isn't needed beyond more speed, it makes it worthy of the HP label. An example was the R/T Dakota's of the late 90's. The 5.9 wasn't changed, but because it was in the lighter 2WD Dakota and had beefed suspension and such, I think it worthy of the label. Another example might be the Ram's that could get an R/T badge by selecting the correct options to spec out a truck that was more speed orientated rather than tow/haul.
Bottom line? My opinion is horsepower rating and/or a sticker/label are marketing and only the parts added make it "HP". Sometimes the parts are in the motor, and sometimes it is a motor and/or suspension added to a vehicle.