The cartridge was introduced in the late 1870's, I believe, and was originally used in S&W top break revolvers, and is still loaded by Remington and Winchester today. As you noticed the case is shorter than .38 Special, it is also wider, as is the bullet, .38 S&W revolvers generally have a bore diameter of .361, .38 Special .357. The British called this round the .380 Revolver, used a 200 grain bullet in their original serive load then switched to a lighter bullet, 178grs I think, and the last version was called the .380MKIIz, its also called the .38 Colt New Police when loaded with a flatter point bullet.
I doubt there would be any collector interest in your ammo, but someone that has a revolver chambered for this round might offer you a few bucks for it. Factory .38 S&W has been going for around $30 a box locally so its not cheap ammo.