The .38 Long Colt was the military round from 1892 to 1911, and was the infamous weak round of the Phillipine insurrection. It is obsolete.
Although the spec for .38 Long Colt is shorter than .38 Special, I've found individual revolvers for it bored long enough for .38 Special or even .357 mangum cartridges to chamber, although neither are safe to fire.
The .38 S&W will fit and fire if the chamber is slightly over nominal spec, which it often is, but it is not designed for it.
The .38 S&W was introduced about 1877 for the S&W .38 double action, and is still available.
It is shorter than the .38 Long Colt cartridge, which is not suitable for .38 S&W chambers.