I do have one oddball combo of the two though, I forget where I got it, but it has a 2 piece metal case like a proper Stanley knife, with the button on top to extend the blade, but the blade it came with, while shaped like the standard Stanley blade, also has places where you can snap off the dull end like a typical box cutter blade. The only difference between it an and actual Stanley knife is that the button throw (and the blade) is much longer. I guess it would be considered a heavy duty box cutter, as opposed to the typical cheap plastic ones.
Stanley is the most common supplier of those knives in the US as well, although the common term is more often "utility knife" for the Stanley, and some call any retractable blade knife a "box cutter" but as I freely admit, if there's anything Americans are, it's inconsistent.