It was billed as being better for shooting at people in cars and in bullet-proof vests.
The .38-44 monniker was intended to show that it was for S&W's built on their .44 frame, not ordinary medium-frame guns.
Nonetheless, Colt "listed" it as being suitable for any of their .38's, including the Detective Special! I think they meant it could be safely fired in them. Extensive use would shake the smaller guns loose fairly soon.
Writers like Skeeter Skelton cautioned that their handloads in this range were meant ONLY for .44- framed guns, including the Colt SAA and the New Service.
I asked S&W's sales manager in the 1960's about this, and he told me that Hi-Speed (.38-44) ammo could be safely fired in the M&P, but that it would shorten the useful life of the gun. He told me that if I expected to shoot much of it, to get a .38-44 or a .357. I think it was good advice.
The USAF shot loose their M-15 revolvers with their hot loads. (Not the US M-41 load, which is mild.) That was a key reason why they wanted a 9mm, and it led to the adoption of the Beretta M-9 in 1985.
If you have not read Elmer Keith's, Sixguns, buy a copy NOW. It will save you asking many questions. Get the later 1961 edition or a reprint. Also strongly recommended is the late Geoffrey Boothroyd's, The Handgun. I think Amazon.com and other Online sellers often have these books.
T-Star