(Disclaimer: the remainder of this article is treknobabble in its purest form and should not be construed in any way, shape or form to reflect reality in any sense. These are fictitious descriptions of fictitious weapons using fictitious science. This is even (mostly) true for descriptions of weapons like lasers and fusion devices.)
The term is commonly held to be derived from PHASed Energy Rectification, but this is most likely a backronym.
Ship-board phasers have been seen set to stun, just like their handheld cousins.
The basic hand phaser (Type I) is a small rectangular box that fits into the palm of the hand. In most versions seen in the various Star Trek series, these can be clipped into a pistol-like unit (the Type II) for increased power and battery life. The Type III designation is used for larger phaser rifles that do not apparently share any components with the Type I or Type II.
They differ from phasers in usually having a different colour beam. One type of disruptor, the Varon-T Disruptor, is outlawed in the Federation because it causes a painful, lingering death; Commander Data was threatened with this in the episode where he was captured by a collector, Kivas Fajo, in the third season Next Generation episode, The Most Toys. Only a few were made, and those were presumably destroyed after Fajo's arrest.
Few other races but the Ferengi, who still employ it on their Marauders, use this weapon. The Romulans disbanded with the weapon, as it was not only dangerous to the target but the very nature of electroplasma meant that the weapon was unstable. Nor did the weapon have a modifiable power strength and could easily destroy a target or an object when all that was desired was to disable them.
A Muon is a stellar sub-atomic that can be caused when cosmic rays strike a dense object, what results is either a neutrino, positron, muon or some other particle. These particles have an approximate lifespan of 2.2 microseconds but can be chronoton-modulated to extend their life spans. These have 207 times the mass of an electron with a similar charge. They have properties similar to that of a neutrino. Star ships require immensely compressed shields to prevent these high-speed sub-atomic particles from slipping through the shielding.
They have variable yield (lower yields used for close range shots) - the yield is adjusted by changing the amount of anti-matter loaded before launch, according to the Next Generation Technical Manual. They have navigation and propulsion abilities of their own, and can thus track an enemy ship. The empty cases have been used for burials at space.
By the time of the Next Generation, torpedoes (emptied from the warhead) can go at warp speed themselves - a diplomat used one in The Emissary (TNG) for transportation, though it was a tight fit. These devices are also used as probes.
Over the years, we've seen torpedoes with many different 'MARK's written on the side, suggesting this technology has undergone continual improvement.
Beam Weapons
Starship Phasers
Phasers are the quintessential Star Trek beam weapon, first seen in the original series. The ship-board variant is known to have existed at least ten years before the time of the original series, and we may have seen them in The Cage as the ship-board beam weapons were not called lasers there.Phaser Sidearms
Hand phasers were first seen in the episode Where No Man Has Gone Before, from the original series. They have a variety of settings, and are quite versatile. They can warm rocks, stun people, cut holes in things, cause burn damage on people and even vaporise things and people outright. From The Wink of an Eye we know that phaser beams do not go at the speed of light, but significantly slower.Phase Weapons
Phaser Weapons were first introduced in Enterprise. They come in two variaties, Starship Based cannon and Small Pistol like sidearm. They most likely use the Slow Nadion effect, rather than the Rapid Nadion effect used in Phasers.Disruptors
Disruptors are employed by the Cardassian Empire, Romulan Star Empire, Klingon Empire, Borg, Breen and Orions in their hand armaments and military armaments as well as being mounted as cannons, arrays, emitters, turrets and banks.Plasma Beam Cannons
These are usually mounted only on vessels and use similar technology to a transporters ACB to emit a beam of highly concentrated, high powered and mildly unstable stream of electroplasma. This weapon was developed by the Romulans and was one of the best-kept secrets from Starfleet and was highly effective against Federation shields and technologies.Phased Polaron Cannons
These are weapons that were first encounter when contact with the Dominion was made. Polarons are Anti-Muons, the antiparticle counterpart of the muon, it is extremely powerful and has an immensely devastating effect against Federation shielding.Lasers
Lasers were seen used as hand weapons in The Cage, the first pilot episode. Since then we have not seen the protagonists using them. In Next Generation episodes, when the USS Enterprise was confronted by enemies using
them as shipboard weapons, they remarked that it would not harm them even with the deflector shields off.Ballistic Weaponry
Fusion missiles
These are the original weaponry carried by the first Starfleet vessels. They involve the primitive use of heavy hydrogen and a high speed particle accelerator. The heavy hydrogen is accelerated and fired into a store liquid supply of heavy hydrogen by the particle accelerator. The heavy hydrogen atoms collide at high speed and release masses of energy this is isolated and the result is that of a helium atom. The resulting energy is greater than a nuclear explosion that occurs on the sun. This weapon was eliminated when shield technology was introduced and when shield technology advanced until it could repel most forms of simple common radiation. Also called Spatial Torpedos.Photonic Torpedos
These torpedoes are the precurser to Photon torpedoes, they most likely use an Anti-Matter Induced detonation to create Nuclear Fusion. They are variable yield devices, it means that you can vary the amount of Anti-Matter used in the warhead.Photon Torpedoes
Photon Torpedoes are a missile weapon usually fitted to Federation vessels, but seen used by many races. They were first seen in the Original Series, and have not been introduced into Enterprise (yet). They are supposed to work by annihilating matter and anti-matter, thus causing a large explosion.Quantum Torpedoes
Quantum Torpedeos were first seen in the Star Trek: Deep Space Nine episode, The Search, fitted to the USS Defiant. They are considered to pack a harder punch than normal photon torpedoes. Fan and backstage material suggests that they are supposed to work by harnessing zero-point energy (a real life concept).Tri Cobalt-Strotium Torpedoes
Tri Cobalt torpedoes were seen in the pilot for Voyager, The Caretaker.
They used to demolish the Caretaker's array. Little is known about them. Some fans have suggested that they are extremely advanced and classified munitions, another theory is that they are for demolition and would not be used in combat.Chronoton Torpedoes
These are chronoton temporally phased torpedoes which shuffle backward and forward in time or even shift right outside the experienced space time continuum. This allows them to slip straight through unmodified shielding no matter how powerful. These Torpedoes are highly specific in temporal variation as not to be lost or erased from space and time. To counteract
temporal weaponry you require temporal shielding where the shield projection matricies are flooded a chronoton variance flow. This blocks against temporal incursion and thus can prevent chronoton torpedoes from skipping through the shields. The only problem with that is with the temporal factor removed from the equation it leaves a fight between superior shields and heavy weapons fire. One very valuable factor of the Temporal shield is that a starship or a starbase can be temporally shielded and thus unsusceptable to timeline alterations. If, for instance, the asteroid that wiped out the dinosaurs was deflected or destroyed and dinosaurs continued to live, all of the timeline after that point would be erased and the only thing left of the previous time line would be that of the temporal shielded facilities and vessels.
See also: Physics and Star Trek, Science fiction weapon