Most sources I’ve read suggest that “gunfighter,” and “gunman” were terms used in the later days of the Old West (probably after the 1870s or ’80s) for someone who was also known as a “shootist,” or in our post-Western movie times, the guy who had the pistol and wasn’t afraid or hesitant to use it.
According to Winfred Blevins’ highly useful “Dictionary of the American West” (to which I’ve referred here before), “gunfighter” and “gunmen” as well as “gunfight” and “gunfighting” all came along in the late 1800s — and there was never any distinction made between “gunfighter” as the sort of good guy or “gunman” as the bad guy. Blevins suggests that such terms almost always referred to pistols rather than long guns, i.e., rifles. (Interestingly, the term “shooting iron” in reference to handguns is found as far back as 1787.)
Term ‘gunman’ first used in print by Bat Masterson in NYC
Blevins says the first use of “gunman” was in a 1903 New York newspaper. The Old West lawman-turned-newspaper-sports-writer, Bat Masterson, also used the term “gunfighter” when he wrote of his Western adventures and told of the people he encountered back in the days of his Western career. The related term “gunslinger” has been traced back to early Western movies, but isn’t authentic to the Old West. It was picked up quickly by Western writers and popularized in novels and movies.
One of the interesting, archaic terms which Blevins says goes back to the days of the American Revolutionary period is “gunsman” — which he says probably wasn’t limited to those who used pistols.
The whole culture surrounding guns was crucial in the days of the Old West, and much that we have romanticized about guns and those who used them came about from actual usage being distorted by the early, flamboyant Western writers (i.e., the dime novelists) then carried into present-day cultural fiction.