From a posting I made several years ago:
This is from the 1939 Winchester ammunition catalog listing:
.357 S&W Magnum Super Speed 158 Gr. Lead 1510 ft/sec 8-3/4" bbl (not 8-3/8")
.38 S&W Special Super Speed 158 Gr. Lead 1115 ft/sec 5" bbl
.38 S&W Special Super Speed 158 Gr. Metal Point 1115 ft/sec 5" bbl
.38 S&W Special Super Speed 150 Gr. Metal Piercing 1175 ft/sec 5" bbl
.38 Colt Special 158 Gr. Lead 870 ft/sec 6" bbl
.38 S&W Special 158 Gr. Lead 870 ft/sec 6" bbl
.38 S&W Special 158 Gr. Metal Point 870 ft/sec 6" bbl
.38 S&W Special 148 Gr. Mid-range lead WC 770 ft/sec 6" bbl
.38 S&W Special 148 Gr. Full charge lead WC 870 ft/sec 6" bbl
.38 S&W Special 200 Gr. Lead, Super Police 745 ft/sec 6" bbl
This is the full product listing for Winchester .38 Special & .357 ammunition. There is nothing identified as .38-44, only the Super Speed loads shown. .38 S&W Special and .38 Colt Special are identical except for the bullet shape (the .38 Colt Special has a flat point). There is no .38 Colt Special Super Speed loading listed.
-------------------------
Addition - I consulted the 1943 Western ammunition handbook. The ballistics information provided is mostly identical to that from Winchester given above. However, it is made clear that the Western .38 Special Super-X load is the same as the .38-44. There are no longer listings for the 158 grain lead and 158 grain metal point bullets for the .38 Special Super-X, only for the 150 grain metal point and 150 grain metal piercing bullets, both at 1175 ft/sec from a 5" barrel. Additionally, there is a second .357 Magnum Super-X load shown using a 158 grain metal point bullet having the same ballistics as the 158 grain lead bullet load (1510 ft/sec from an 8-3/4" bbl). No .38 Colt Special loads are listed.
I'd bet that virtually identical ballistic information would be found in Remington publications of that time period, except that Remington's equivalent to Winchester's Super Speed and Western's Super-X is called "Hi-Speed."
Incidentally, the first appearance of the .357 Magnum was in Remington's January 13, 1937 dealer price list. It was available from them only in a single loading with a metal point 158 grain bullet. Note: Metal point refers to a metal cap over the exposed part of the bullet, with the bore bearing surface being lead. It is not a FMJ, even though it looks like one. That bullet design was common then in several calibers, as it was believed to reduce bore wear.