Both .38-44 and .38/44 are seen, and I am not sure what the most “correct” designation is, or if there even is one. The use of.38-44 is a little misleading as the “44” could be interpreted as the propellant charge, such as .44-40, .38-40, .32-20, etc. The .38/44 as a designation would be more expressive of its use in a .38 Special revolver built on a .44 frame. Headstamped cartridges are not that unusual, but if one had a full box of .38/44 cartridges in good condition , it would be in high demand as a companion piece by a S&W collector having a S&W Heavy Duty or Outdoorsman revolver. Collectors of old handguns like to have a nice box of correct ammunition of the same period as their revolver for display, not for shooting, and would likely put a higher value on it than would a cartridge collector. Otherwise, I have no idea of the value of a single round. I wouldn’t think very much.
I have some reloading manuals from the 1940s and 50s, and they do not refer to it as either .38-44 or .38/44. They call it the .38 Special High Velocity, noting that it should be “used only in large frame revolvers.” The velocities given are usually around 200-300 ft/sec greater than their standard.38 Special load recipes. That sounds like probably a .38/44 load to me, and I think some Remington .38/44 ammunition boxes of the time are labeled as “.38 Special Hi-Speed.” Others can comment more knowledgeably than I about that.