The .38 Long Colt cartridge was originally introduced as a round to be used in cap & ball > metallic cartridge conversions. The U.S. Navy adopted it and had Colt convert their inventory of model 1851 revolvers. At the time the round had a heeled bullet similar to the kind used in .22 L.R. cartridges today. Because the case and bullet were the same diameter, chambers were bored straight through.
Later, the .38 Long Colt was offered in various models, including the Colt 1889 Navy (1889-1894) and the 1892 New Army & Navy (1892-1907).
Meanwhile, in 1899 Smith & Wesson came out with an improved version of the .38 Long Colt, which they called the .38 Smith & Wesson Special. It quickly became popular because besides the .38 Special one could also use the shorter length .38 Short and Long Colt cartridges in the same chamber(s).
But the .38 Special didn’t use a heeled bullet, so the chamber was stepped down to bullet diameter in front of the case. This is still true today.
Both the Army and Colt had by this time abandoned the heeled bullet, and late production model 1892 Colt’s had stepped chambers.
In 1908 Colt introduced what they called the “Army Special” even though neither the Army nor Navy ever adopted it. These were chambered in .38 Special, not .38 Long Colt, although Colt called the round, .38 Colt Special because they had no desire to stamp “S&W” anywhere on one of their products.
If a Colt double-action .38 revolver has a straight bored through chamber, and is marked .38 D.A. on the side of the barrel, it is intended to be used with either .38 Short or Long Colt cartridges, not .38 Special. The .38 Special will fit, as will some .357 Magnum rounds. Because they fit however, doesn’t mean they should be used.
You can safely fire .38 Short or Long Colt’s in a revolver chambered in .38 Special, but not necessarily the other way around.