Note: There is no “FTL drive” of any sort in this setting, sorry.
Conversion Drive: The primary means of interstellar travel in the Federation and most surrounding systems. Magnetic monopoles are passed through a mass of hydrogen, the atoms the monopoles come into contact with are converted to antimatter which reacts with the surrounding hydrogen, catalyzing a fusion reaction that provides thrust. In theory it is safer than normal antimatter-catalyzed fusion in that it does not require carrying a large quantity of antimatter but merely a small amount of re-usable monopoles. The thrust achievable is far greater than normal fusion torches and acceleration exceeds that of solar sails. A typical cruising speed for interstellar voyages is half the speed of light, but velocities up to .7c have been recorded.
*May 2018 update, it currently appears that the “EM Drive” was just noise from Earth’s magnetic field, consider this non-canon for the time being* Casimir Thruster: In the early 21st century a low-thrust reactionless drive was discovered, it took most of that century to make practical use of the concept though. Regardless, it became invaluable to space travelers. Ships did not need to carry as much bulky reaction mass, all they needed now was a power plant and fusion power had made that far more simple. It was nowhere near fast enough for interstellar travel within the projected lifespan of civilization, and it could not provide enough thrust to rise more than a few centimeters above the ground of an Earth-size planet, but it was enough for regular travel within a star system.
Stargates: A typical stargate is a ring with a 10-kilometer diameter. But the actual mouth of the wormhole is a 500-meter sphere located at the precise center of the stargate. The stargate has no control over the actions of the wormhole, it simply marks its location and provides a base for the Federal Guard who defend the wormhole, or the system on the far side. Ships can enter a wormhole from any angle and come out the other mouth, but for convenience’s sake most stargates are oriented perpendicular to the solar system’s plane so that ships coming from a planet in the system can make a more-or-less straight run through the ring. They rocket out from one star system, pass through a wormhole, and keep on going into the interior of the next system. Most details on the construction of wormholes are considered top secret, but what has been revealed is that when the route is first laid down the wormhole is very narrow, measured in nanometers, and the mouths are transported in magnetic bottles. When both mouths are in place they are released and large quantities of “exotic matter” are fed into the more coreward mouth, somehow, this props the wormhole open and expands it slowly over the course of several years before finally it reaches its full .5km diameter. For some unknown reason every wormhole mouth has been placed no less than 100 astronomical units from a celestial body of planetoid size or greater, there are many hypotheses why this is, most of them are not good. Some say that wormholes are inherently unstable and only need a little “push” to explode with enough force to shatter nearby planets, others say that they conflict with significantly sized gravity wells, or perhaps the Federation wants to delay potential invaders who might think of using their technology against them, a lot of people think it’s a mixture of all three. Regardless, the overall effect on society is that a conversion drive starship at full throttle takes at least a week to reach a stargate from the inner system of a Sol-type star, a couple hours if they had came in from interstellar space without decelerating, while most stargate-network exclusive craft with Casimir drive take a month or two.