The term rocket generally refers to a medium that carries such objects as satellites, spcae probes etc., into space. But they never go into orbit. The fuel burnt inside a rocket produces high-energy gases. These gases emitted through the rocket's tail push it upwards into the sky. Different rockets can reach different altitudes in the sky, and they are generally not reusable.
On the other hand, space shuttle is a partially reusable space vehicle that can carry astronauts and large objects well into space. To reach its destination, a space shuttle needs the help of booster rockets. Space shuttles are limited to low-Earth orbits.
However, many space agencies are now trying to develop reusable rockets.