The difference between .38 S&W and .38 S&W Special. Handgun manufacturers, in order to capture new revenue streams and keep their products from being copied, introduced new models with a different caliber from time to time. In 1876, S&W introduced the top break .38 Single Action, also called the Baby Russian. This gun was chambered for S&W's new centerfire cartridge, the .38 S&W. The .38" was the diameter of the casing and the bullet was .360 in diameter. Of course, it was loaded with black powder but was still a rather anemic cartridge by today's standards. But, it provided a more powerful cartridge than the .32 rimfire and .32 S&W centerfire cartridges. S&W rapidly expanded their product offerings for this cartridge which were very popular. So popular that the British adopted it as the .38 Webley and made it their standard sidearm cartridge from the 1870's up through WWII.
In the late 1800's, the standard US Army cartridge passed from .45 Colt to .38 Long Colt which was a smaller diameter cartridge than .38 S&W. However, the Philippine Rebellion in 1896 and the Tagalog Insurgency showed up the .38 Long Colt for the anemic round it was. So, seeing an opportunity to capture the Army contract with a new round, they stretched the .38 Long Colt casing which added more black powder and thus, more power. In 1899, they introduced .38 S&W Special and the 1st Model .38 Hand Ejector, AKA the Army-Navy Model. Thus, .38 S&W Special is, like the .38 Long Colt, a smaller diameter but longer cartridge than .38 S&W. They are close enough in size to allow .38 Special to be shot in cylinders chambered for .38 S&W but reamed to allow the longer cartridge to fully insert. As K22 shows, .38 Special will swell and may crack when shot in the larger diameter .38 S&W cylinders. If you reload, this is a problem for reusing the shell, but it is not a safety problem.