It IS the 38Spl, for three reasons:
More power (usually!)
More available weight.
Better hollowpoint designs because with no "feed ramp", bullet shapes can feature radical noses that would jam up an auto.
That latter is one reason the best 38Spl+P rounds can do as much damage as even the better 9mm rounds, even though the 9mm has more energy on tap.
However! From a snubby (2" barrel), the 38Spl and even 38+P are somewhat marginal. You have to be picky about your ammo...there's a lot of absolute junk out there. Some of the best: Remington's 158+P, any of the (expensive!) Buffalo Bore, the Speer Gold Dot 135+P, Winchester's 130gr "Supreme" +P, the Hornady Critical Defense in both standard and +P, Cor-Bon's "DPX" 110gr. The Remmie 158+P is a bargain for the performance delivered; the only standard-pressure 38 (read: "not +P") I trust is either Buffalo Bore's 158 or 125 if I can afford 'em, or the Hornady Critical Defense if I'm on the cheap.
Buffalo Bore's 38+P 158gr slug is THE king of the hill in terms of 38Spl energy. From a 2" barrel it gives as much energy as most 9mm
from a 4". It's shockingly good stuff for "when you care enough to send the very best".
As to:
I don't have any .380 ammo, so I put a 9mm (which is 2mm longer than a .380 ACP) on the left next to a 38 Special on the right. That should pretty much answer your question!
Meaningless, because the 38Spl is a late-19th-century design originally meant for black powder, which is very bulky for it's power level. The 9mm and the .380 designed shortly after the 9mm) are early 20th century designs meant for modern smokeless power, and hence use much more compact shells.
Other "black powder ancestry" calibers that are as a result "oversize" are the 45LC, 44Spl/Magnum (as they're stretched from the .44Russian), 357Mag (stretched from the 38Spl), 38-40, 44-40, 45-70 and a surprising number of others.