The original .38 cartridges WERE .38 bore...
This is best explained by having you go find a complete loaded .22LR shell, unfired, with bullet in it. You'll notice that the part of the projectile that actually gets spun by the barrel is as "fat as the shell itself". So the projectile is .22, and the shell is .22 bore.
That is a very old style of making shells, only seen today in the .22LR and the .22short.
Most shells used to look like that, circa 1863 - 1895ish.
If you measure the shell on a .38Spl or .357, you'll see it comes very close to .38 bore. Go back far enough, late 19th century, and you'll find .38 shells that fired from a .38 bore and fired .38 projectiles.
The problem with that system is that the area of the projectile that rubs against the rifling during firing can't hold a whole lot of lubricant. As the power levels rose, this became a major problem.
The solution was to drop the bore to the point where the bullet could properly back down into the shell. That allowed lots of lubricant to be stored in grooves protected by the shell. But the bullet (and bore) had to get narrower. By the early 20th century, the .38Spl was actually a .357 projectile. They didn't want to call it a ".36Spl" because it was actually more potent than the earlier, more primitive and fatter .38s that it replaced, but if they called it a ".36Spl" people would think it was weaker.
So it was all marketing, but for pretty valid reasons.
The ".44" is the same way - most are about .429.
By the time the .357Magnum hit in the mid-30's, people were used to the idea of a small-bore projectile moving at rocket speeds. S&W had chambered a large-frame gun originally made for the .44Spl to .38Spl, and people were selling super-hot loads especially for that critter that were about on par with the very best .38+P sold today. People loved it - the .357Magnum was that same basic concept taken to "the next level". The rep of the .38/44 just prior had "paved the way" for the .357Mag.
Jim