The Space Shuttle Main Engine uses the RS-25 designation.
The RS-25 was NASA’s reusable liquid-fuel engine for the Space Shuttle orbiter and is also used, in updated forms, on the Space Launch System. Each Shuttle orbiter carried three engines at its aft end, supplied with liquid hydrogen and liquid oxygen from the external tank.
Rocketdyne developed the engine during the 1970s using a high-pressure staged-combustion design. The first flight-ready versions powered STS-1, the Shuttle’s first mission, on April 12, 1981. During ascent, the engines could throttle over a wide range and gimbal to help steer the vehicle, while the two solid rocket boosters supplied additional liftoff thrust.
The alternatives are engines associated with other launch systems or eras. RL10 powered upper stages, J-2 powered Saturn upper stages, and F-1 powered the Saturn V first stage. The name “SSME,” meaning Space Shuttle Main Engine, was widely used during the Shuttle era; RS-25 is the formal engine designation. Modern RS-25 variants support SLS missions, though those engines are expended with the rocket rather than recovered for reuse.