Thomas, The .38-40 Winchester is actually a .40 caliber cartridge shooting .401 caliber bullets. The cartridge was introduced by Winchester in 1874 and is derived from their .44-40 Winchester. This cartridge was introduced for rifles, but in its reintroduction for Cowboy Action Shooting it has seen some popularity as a revolver cartridge. It is not particularly well suited to hunting larger game, but it was popular when it was introduced, along with the previous .44-40 Winchester, for deer hunting. It can be used successfully on smaller game animals, and for self-defense. Ballistically, commercial 'cowboy' loads are similar to the much newer .40 S&W, sharing the same bullet diameter, bullet weight, and similar velocity. A limited number of 'hunting' loads are available commercially, which produce about 25% more muzzle energy than the more common target ammunition.

.38-40 Winchester is an old (hard to find) round that is used in cowboy action shooting. It has the same performance as the standard .357 magnum. I recommend getting this pistol in .38/.357 magnum as ammo is significantly easier to find and affordable. I hope this helps!