The Star Frontiers Basic Game Rules say this in its basic equipment section:
Laser Pistols fire a pencil-thin beam of intense energy in a burst that lasts only a fraction of a second. Each powerpack contains enough energy for 20 shots. Laser pistols are the most common sidearm on frontier worlds, and are often called "blasters". [SF Basic Game, p. 9]
So by this line, we see that in the Star Frontiers campaign universe, blasters = laser pistols, with their "pencil-thin beam" of light energy. It seems pretty obvious that this was intended to make a mental connection with the popular Star Wars films that had come out in the years immediately prior to the game's publication, where all of the sidearms are referred to as "blasters":
OBI-WAN: Your father's light saber. This is the weapon of a Jedi Knight. Not as clumsy or random as a blaster; an elegant weapon for a more civilized age.
HAN SOLO: Hokey religions and ancient weapons are no match for a good blaster at your side, kid.
BARTENDER: No blasters! No blasters!
It's certainly the case that the stock sci-fi weapons in Foundation are called "blasters" or "blast pistols":
Toran opened the inner door and closed contact on his blast pistol... He [Pritcher] held his hands apart, "I'm not armed, and I come on a peaceful errand. You might relax and put the blast pistol away."... There was an irresolute silence and then Bayta said, calmly, "Put the blaster away, Toran, and take him at face value. He sounds like the real thing." [Book Two, p. 144]But what is their effect when fired? Here's one demonstration:
Devers snarled and reached slowly for his own gun. The lieutenant of police smiled more broadly and squeezed the contacts. The blasting line of force struck Devers' chest in an accurate blaze of destruction -- that bounced harmlessly off his personal shield in sparkling spicules of light.And here's another:
Devers shot in turn, and the lieutenant's head fell from off an upper torso that had disappeared. It was still smiling as it lay in the jag of sunshine which entered through the new-made hole in the wall.
It was through the back entrance that they left. [Book Two, p. 92]
Bayta, face frozen white, lifted her blaster and shot, with an echoing clap of noise. From the waist upward, [X] was not, and a ragged hole was in the wall behind. From numb fingers, Bayta's blaster dropped to the floor. [Book Two, p. 273]
I have to agree with Obi-Wan here -- this is distinctly not "an elegant weapon". While the first example speaks of a "blasting line of force", the end result is tremendously more destructive than anything we see in most sci-fi games or movies -- it wipes out someone's entire torso, leaving limbs and head bouncing separately on the ground, in addition to taking out most of the wall behind them. Or it disintegrates everything on a person above the waist. Stuff like that -- it's freakin' brutal.
Now, of course, when Asimov was writing in the 1940's, lasers didn't exist yet. The first functioning laser was not constructed until 1960 (although theoretical principles do date back to Einstein in 1917; link), and it was only after this point when the "laser" seemed to become the obvious choice of sci-fi armaments. In Foundation, it seems like the "blaster" functions more like a mini-nuclear bomb blast. You can almost see the man-sized mushroom cloud erupting from where a person used to be -- and certainly this is line with Asimov's fetishization of all things atomic-powered at the time.
But we can see that the overall evolution of the device -- from works like Foundation to Star Wars to Star Frontiers, etc. -- is one of radical diminution of the effect, starting from almost complete bodily and area destruction, and ending with a mere "pencil-thin beam" that does some amount of localized harm to the target, all under the same name -- and following the trends of real-world technology of the time.
Can you find any earlier literary examples of "blasters"?