A meteoroid is usually taken to be ANY naturally occurring body that will eventually enter a planet's atmosphere (whether it will survive to impact is irrelevant). The word is also used by some astronomers to denote any small extraterrestrial body floating in space with no dimension greater than a kilometer: close to 2/3 of a mile, which is meant to distinguish it from the larger asteroids.
Asteroids are chunks of material floating in orbit around the Sun, which, unlike comets, almost always lack a liquid or gaseous component. They are commonly composed of iron, carbon, silica, nickle, magnesium, etc.