A spaceship or starship is any manned spacecraft that has the ability to transport and support a crew across space. It flies using an internal engine and propellant fuel as opposed to a spacecraft which is propelled by an external force.
For interstellar distances, starships use faster-than-light spacecraft propulsion technology, such as warp drive. This is a Type II technology. An iconic starship was the USS Enterprise in Star Trek. The Enterprise used an impulse drive when not in warp, and this used fusion reactors. This needed inertial dampers, or inertial dampeners, to counter the effects of rapid acceleration and deceleration by sustaining and absorbing the natural inertia of a vessel, as the rapid acceleration would smash the crew into the walls, killing them instantly.
A bioship is an organic spaceship.
An interstellar ark is a spaceship designed for long-term interstellar travel, such as a generation or sleeper ship.
For vast galactic distances or beyond, spaceships need to enter natural or artificial constructs like wormholes or hyperspace. Type III civilizations and beyond might consider a black hole starship or methods of instantaneous teleportation such as a tachyon spaceship.