An asteroid is an object in the asteroid belt. A meteor is an object that burns up in the atmosphere, a meteorite is an object that hits the ground, and a meteoroid is an object in space. So an asteroid is just a different type of meteor/oid/ite.
Agree with you and Tigerseye except the definition of asteroid is orbiting the sun, most but not all being in the asteroid belt. So agree upon entering the atmosphere it was a “meteor”. I’m not certain of NASA’s clarification that it was a small asteroid, however other things can enter the atmosphere such as a comet though again they orbit the sun and can be viewed as icy asteroids which produce a visible tail.
Mostly nomenclature I guess, however they said this one probably traveled a year before hitting us. Because it must have been in space for millions of years, I think they mean it got deflected inward from the asteroid belt, probably by an impact with another object.
This baby came at us much faster on a different path than the near miss asteroid so it’s sobering to think a deflection can head for us on short notice and go unnoticed till impact.
Does the whole meteor/ite/oid thing apply to comets, too, or just asteroids?
It looks like there is a continuous range of sizes from very small meteors to the largest asteroids, and where we draw the line between "meteors" and "asteroids" is a matter of semantics. We can say that a meteor is an object up to a certain size and anything larger than that is an asteroid. They are all objects in space subject to the law of gravity.