All modern Starfleet ships are fitted with a quantum slipstream drive, enabling a ship to travel at the fastest it can go for a short period of time. This is exceptionally useful for ships in emergency situations, such as when responding to a distress call.
A quantum slipstream drive creates a slipstream in front of and around a ship, enabling it to cruise at maximum velocity. This is regardless of what a ship's own warp core can handle; the slipstream drive enables it to push warp 9.99 regardless as it does the work instead of the warp core. It routes energy through the ship's deflector to create the quantum field, constantly adjusting phase variance and penetrating the quantum barrier.
Due to the high energy usage, a quantum slipstream drive can only run for a certain amount of time and afterwards, has a cooldown time. These figures depend on the type of ship it belongs to; larger, more powerful ships have a longer runtime compared to ships that cannot sustain that amount of energy usage for longer durations.
The USS Eventide travelling via quantum slipstream
In modern day usage transwarp does not refer to warp ten, the phenomenon where you are travelling at infinite velocity and occupying every space in the universe at once. Instead, it refers to the ability to create a transwarp corridor or tunnel between your ship and the closest transwarp gate.
The Federation Transwarp Network was opened in 2399. At present there are five transwarp gates that can be utilised. These are located in the Vulcan Sector, Azure Sector, Qo'noS Sector, Bajor Sector, and Alsuran Sector. Transwarp gates work on a point-to-point basis; they do not let you transwarp to any point in the universe. You can jump to a gate and use it to go to another gate, but nowhere else.
In order to access a transwarp gate, a ship needs to be fitted with a transwarp coil. When engaged, this automatically creates a connection to the closest transwarp gate which opens a transwarp corridor. The gate itself does most of the work, as a ship would not be able to produce enough energy to cross all of that distance itself.
Each faction has its own type of transwarp coil. Gates are coded to accept only these forms of transwarp coil - so no unauthorised person could take advantage of the network - and factions' transwarp coils can be blacklisted at any time. This is in order to prevent mass fleet movements to a location if conflict was to break out between any of the factions.
Sector map including transwarp gates