The Star Trek Online Wiki has a wonderful description of each damage type, I've copy and pasted them below (in case the website goes boom).
Phaser damage is displayed as an orange colored beam. It is a directed energy primarily used by the Federation for both ground and space weaponry, although in-game any race or faction can use Phaser energy weapons. The term "phaser" is an acronym for Phased Energy Rectification. Player-acquired starships for the Federation by default come with Phaser energy weapons. Shields and armor with the [Pha] suffix modifier take 20% less Phaser damage than usual.
Energy bonus: 2.5% Chance: Disable 1 Subsystem for 5 seconds (Space) / 5% Chance: +2 Hold
Disruptors are a type of directed energy used in weapons, and are green or dark green in color. They are used by races such as the Romulans, Klingons, Gorn and Orions. There are multiple types of Disruptor energy ranging from Type 1 to Type 3, although in-game there doesn't appear to be any difference between Disruptor energy weapons. Disruptors cause damage to the target by breaking the bonds of atoms. Shields and armor with the [Dis] suffix modifier take 20% less Disruptor damage than usual.
Energy bonus: 2.5% (Space) / 5% (Ground): 10% Damage Resistance Debuff
Plasma energy beams are emerald in color. Plasma projectiles are typically seen in use by Romulan, Cardassian and Borg vessels and weapons platforms. High-yield Plasma projectiles are extremely powerful. Focused beam Plasma energy is not directly used by any one race or faction in the game. Shields and armor with the [Pla] suffix modifier take 20% less Plasma damage than usual.
Energy bonus: 2.5% (Space) / 5% (Ground) Chance: Applies a non-stacking DoT
Tetryon energy beams are blue in color. Tetryon weapons are not specifically used by any race or faction, but they are available to anyone. Tetyrons are subatomic particles that exist outside of normal space. When brought into normal space from subspace (artificially or naturally) they become highly unstable. Shields and armor with the [Tet] suffix modifier take 20% less Tetryon damage than usual.
Energy bonus: Bonus damage to Shields (Ground and Space)
Polaron directed energy was heavily utilized by the Jem'Hadar during the Dominion war on both their starship and ground weapons. In Star Trek Online they are pink/purple in color and are available to all races and factions. They are first available to players at the Captain rank (Mk VIII). Polaron ground weaponry typically leaves an anticoagulant behind, although this isn't the case in the game. Shields and armor with the [Pol] suffix modifier take 20% less Polaron damage than usual.
Energy bonus: 2.5% Chance: -25 power to all Subsystems (Space) / 5% Chance: Weapons Malfunction for 5 sec (Ground)
Antiprotons, when confined into a beam, are normally yellow in color; however, in Star Trek Online it appears near identical at distance to Phaser energy 1 and the differences are only apparent up close.  Up close, the energy looks a lot more unstable, similar to Plasma and Tetyron energy. Antiproton beams were used by the planet-destroying Doomsday Machine. In the game, Antiproton energy is used on end-game weaponry. Shields with the [Ap] suffix modifier take 20% less Antiproton damage than usual.
Energy Bonus: +2% Critcal Chance +40 critical severity
In Star Trek Online all types of torpedoes and mines use Kinetic energy as a form of damage. Kinetic energy is highly negated by shields both in ground combat by a Personal Shield and space combat by a Shield Array. Kinetic energy is produced from the reaction of any explosion.
Although projectiles are based on Kinetic damage they do have some differences; for example, Quantum Torpedoes and Mines use plasma-based warheads, whereas Photon Torpedoes and Mines use a standard matter/antimatter warhead. All projectiles are fully based around Kinetic energy damage.
Energy Bonus: none