A little history on the subject...
During the 1920s law enforcement wanted more power than the regular .38 Special, but did not want to step up to .44 Specials or .45 Colts.
S&W responded by working with ammunition companies to increase the working pressure of the .38 Special. These loads were forerunners of what became the .357 Magnum, but the case length was still the same as the .38 Special.
To differentiate these higher pressure loads from regular .38 Specials, the new load was called the .38/44. This was to denote that this load was not to be shot in any .38 Special gun other than those built on the .44 frame (N frame).
In 1930, S&W started making the .38/44 Heavy Duty. This was a fixed sight N frame revolver that looked like a .38 Military & Police on steroids. Most made were 4" but some 5" were also made.
In 1931 S&W brought out a target version called the .38/44 Outdoorsman.
The best solution was the .357 Magnum, which S&W introduced in 1935.
The .38/44 was continued and eventually the Heavy Duty became known as the Model 20.
So when the .38 Special +P was introduced, it was a similar concept. How to put more power into the .38 Special. However, the load was still less powerful than the .38/44, because it was designed to be fired in frames smaller than N.
Going back even further, about a century ago Winchester started making WHV rifle loads. This stood for Winchester High Velocity. A classic example is the .32-20 WCF, which was loaded in a smokeless version that duplicated the old blackpowder load, and a higher pressure version with much increased velocity, hence the name.
The problem is that even though the cases were marked .32-20 WHV people were putting them into cheap weak single shot rifles or into their .32-20 S&W revolvers. This was way too much pressure for what was basically a K frame of the day, and most old .32-20 S&Ws are simply beat to death. Modern steel now gives us the ability to have K and J frames chambered for .357, .32 H&R Magnum, and .327 Magnum. I wish S&W had made a modern 32-20 because it would be an ideal companion to a .32-20 lever gun.