Most of the space rocks are found in orbit around the sun. That orbital path is called the Asteroid Belt the other name for space rocks floating out in space is also Asteroids, smaller space rocks are called Meteoroids.
Any space rocks that has a diameter smaller than 1.6km is called a Meteoroid.
The picture above is drawn with artistic license, so please take it up with the proper authorities.
Sometimes the orbital path of a space rock would fall outside the Asteroid belt and come closer to earth than usual. Sometimes the gravitational pull from Earth may pull it even closer, and sometimes the gravitational pull of it may even cause the poor space rock to fall onto the surface of Earth at such great speed that the rock may create a streak of fire forming a long tail. We call this phenomenon "shooting stars" or meteors, we never call them asters. Occasioanlly if the space rock is large enough, or is made of denser substances like Iron, they may survive the journey all the way from space and smack right into Earth forming a crater. The left over space rock that survived is called meteorite.
This is the artist's childlike impression of a particularly large shooting star.