Colt made a gun, and chambered it for 38 Colt. Later that round was lengthened, and named 38 Long Colt. Because there was now a "Long Colt", people started calling the first one "38 Short Colt", but that is not really the name. Just "38 Colt".
This is Long Colt, but the only difference between Long Colt and Colt is length. Notice the diameter of the loaded round is .381"
Smith and Wesson invented a gun and chambered it for 38 Smith and Wesson.
Notice the diameter of the loaded round is .386"
The S&W was a better round. More people made guns chambered in 38 S&W. Pretty much the only guns chambered in 38 Colt were Colts.
Eventually even Colt quit making guns in 38 Colt, and started making guns in 38 Colt New Police (that's 38 S&W loaded with a flat-pointed bullet). They did that because they did not want to put the competition's name on their guns, so they could stamp them that they were chambered in 38 Colt NP.
You can shoot 38 Colt in a gun chambered for 38 S&W. Normally all that will happen is the case will swell greatly (since it is very undersize). In some guns the case will split.
I, myself, advise against the practice, but many people do it, and will undoubtedly continue to do it.
Meddle not in the affairs of dragons, for thou art crunchy, and taste good with catsup - George of Lod, Year of Our Lord 297
I always take precautions.
Beware the Evil Bullet Fairies.