The .38 Long Colt, which can be used in .357 magnum revolvers, was introduced in 1875.
The .38 Special, which also can be used in .357 magnum revolvers was introduced in 1902.
They are both slightly longer versions of the .38 Short Colt, which was the original ammo for .36 cal cap and ball revolvers converted to cartridges, though they most likely didn't call it the Short Colt until the Long Colt came out.
So you can see that the .36 Colt Navy cap and ball revolver is the great great great grandfather of the .357 magnum revolver.