The shorter .38 S&W dates to 1877 while .38 S&W special was introduced in 1899. The two do not interchange because the.38 S&W has a few thousandths larger diameter case and bullet. There is a much greater variety of .38 special loads on the market and they are a lot easier to find in stock. Usually only the largest gun stores will have .38 S&W and it will be more expensive. Most folks don't consider the .38 S&W to be powerful enough to be a good choice for self defense, but the British Empire used it as their primary military hand gun cartridge from the mid-1930s through WWII.
The two are not interchangeable and should not be fired in the wrong revolver.
.38 S&W
Designed by S&W in 1877
Bullet diameter .361"
Neck diameter .3855"
Base diameter .3865"
Rim diameter .440"
Rim thickness .055"
Case length .775"
COAL 1.240"
.38 S&W Special
Designed by S&W in 1898/1899
Parent Case .38 Long Colt
Bullet diameter .357"
Neck diameter .379"
Base diameter .379"
Rim diameter .44"
Rim thickness .058"
Case length 1.155"
COAL 1.55"