Other forms: spaceships
A vehicle that travels outside the earth's atmosphere is a spaceship. If you want to walk around on the moon some day, you'll have to get there in a spaceship.
Any craft that carries people or equipment through space is a spaceship, though you could also call it a "rocket ship." Traveling through the universe, far from Earth or just outside its atmosphere, definitely requires a spaceship. Spaceship was originally borrowed from 19th- and 20th-century science fiction, and even today the term is considered less scientific than spacecraft or space vehicle.