The pistols used by Starfleet in the 2250s and the 2260s were designed with multiple power settings. They had enough power to blast through rocks, security glass and to disintegrate Humanoid-size androids for example. The laser pistol was also capable of being set to overload, resulting in a forced chamber explosion. These weapons were considered "old-style" by the end of the 2260s. (TOS: "The Cage", "What Are Little Girls Made Of?", "A Private Little War")
In 2254, after having been kidnapped by the Talosians, Captain Christopher Pike attempted to use laser pistols to blast his way out of his cell, but was distressed to find that the lasers were empty. He correctly deduced, though, that the Talosians had been using their powers of illusion to make Pike believe that the lasers were inoperative, and he had successfully breached the cell he was being kept in. Later, after escaping to the surface, Number One set her laser to overload, informing the Talosian Keeper that Humans would rather die than live in captivity. This, combined with information they had assimilated from the USS Enterprise's historical records, convinced the Talosians that Humans were too unstable to be held against their will. (TOS: "The Cage")
In 2261, laser pistols were standard equipment for the Crater expedition to M-113, as well as the Korby expedition to Exo III, both of which were outfitted in the same year. The hand lasers were still in use in 2266. (TOS: "The Man Trap", "What Are Little Girls Made Of?")
In 2265, Spock and other members of an Enterprise landing party were armed with laser pistols when they transported to the planet Delta Vega to maroon a dangerous Gary Mitchell. (TOS: "Where No Man Has Gone Before")
In the story outline for "The Cage", one of the Laser guns was set for a hypo-pellet, whereby "death is instant, painless." (The Making of Star Trek, p. 63) This seems to be a variation on a statement from the series outline Star Trek is..., which proposed that the pistols in the series (as well as the series' rifles) were to fire "hypodermic pellets which stun or tranquilize."
In the first draft script of "The Cage", the effect of the Laser pistol firing was described as "a blinding white thin shaft of light from the barrel of the pistol." In the episode's second revised final draft script, however, this wording was changed to "a blinding thin white shaft of light from the pistol." Evidently, the beam was ultimately colorized red, however.
According to The Making of Star Trek, Gene Roddenberry was made aware by a technical adviser of the fact that lasers could not do the things he wanted his fictional weapons to do and invented the term "phaser" to use instead.
In Star Trek, the crew of the USS Kelvin were equipped with phaser pistols  in 2233. The ship is also seen using phaser banks. In "Obsession", it was also stated that Lieutenant James Kirk manned the phaser station aboard the USS Farragut in 2257. The laser pistol was seen in use in "The Cage" (and "The Menagerie"), set in 2254. They were also seen as part of the away team arsenal along with the phaser rifle in "Where No Man Has Gone Before" set in 2265. All these appearances indicate that hand-held laser weapons were used simultaneously with hand-held phaser weapons in the 2250s and early 2260s.
The original prop was designed and produced by Wah Chang's Project Unlimited, Inc. in 1964 for the pilot production, "The Cage". Close examination reveals the controls on the side are painted typewriter keys. The prop was slightly modified for its later appearances in "Where No Man Has Gone Before", "The Man Trap", and "What Are Little Girls Made Of?". They contained a tiny flip-up sight on top and the barrel could be extended with a twisting/ratcheting motion for greater power. (TOS: "The Cage", "What Are Little Girls Made Of?")
This prop was modified by the addition of a wheel-like attachment on the back of the body of the weapon and a textured grip. While no dialogue in any episode after "The Cage" indicates whether the pistols were lasers or phasers, a stage direction on page 18 of the revised final draft of "What Are Little Girls Made Of?" called for an old-style phaser to be used by Brown. It is noteworthy that this weapon vaporized the android Kirk in a manner more consistent with phaser technology than lasers.