There seem to be different opinions on how to define meteoroid. One big difference between meteoroids and asteroids is that asteroids don't regularly enter the atmosphere. So there's no real need for special words to describe an asteroid in the atmosphere and after impact.
For ("small") asteroids that do impact, NASA actually says that they can be called "meteorites."
The main criterion for distinguishing meteoroids from asteroids appears to be size. Wikipedia's article on "Impact event" uses the criterion that meteoroids are "Objects with a diameter less than 1 m (3.3 ft)." Other sources that I've found describing the difference:
The official definition of a meteoroid from the International
Astronomical Union clearly brings out the distinction between
meteoroid and asteroid: A meteoroid is a solid object moving in
interplanetary space, of a size considerably smaller than an asteroid
and considerably larger than an atom.
Both asteroid and meteoroid refer to bodies in our solar system that
orbit the Sun but are not large enough to be deemed planets.
Traditionally, anything smaller than ten metres across was called a
In space, a large rocky body in orbit about the Sun is referred to as
an asteroid or minor planet whereas much smaller particles in orbit
about the Sun are referred to as meteoroids. Once a meteoroid enters
the Earth's atmosphere and vaporizes, it becomes a meteor (i.e.,
shooting star). If a small asteroid or large meteoroid survives its
fiery passage through the Earth's atmosphere and lands upon the
Earth's surface, it is then called a meteorite. [bolding added]
–NASA's Near Earth Object Program FAQ
An asteroid is a solid body in Space, smaller than a planet but large
enough to be seen at a distance.
A meteoroid is a solid body in Space, too small to be seen at a
distance, which is discovered when it strikes something (such as the
atmosphere of a planet or the surface of another body), causing a
momentary flash of light (a meteor) or other disturbance in whatever
it strikes, or after it makes a crater or deposits meteoritic
–"Meteoroids vs Asteroids", by Jeff Root, at Jeff's Space and Science Pages hosted by the Minnesota Space Frontier Society
(The above seems to be the author's advocated definition, rather than a single established definition.)