As I remember the fixed sight model was known as the "38/44 Heavy Duty" while the target sighted version was the "38/44 Outdoorsman."
The "38/44" designation came from the .38/44 Special cartridge, the equivalent of the +P of its day. The designation meant it was intended for the 44 framed revolvers.
As a matter of interest, there were two .38/44 cartridges: The .38/44 Special which was the high velocity version of the .38 Special, and the .38/44 Smith & Wesson. This latter cartridge was so named as it was a .38 cartridge intended for use in the .44 framed S&W No. 3 target revolver. The case length was full length of the cylinder, with the bullet nose flush, or just below, the case mouth.