Oh, wait... That linked name is completely reasonable and descriptive. It's not like the others.

has a better ring to it than "crashing into the side of a mountain"

It doesn't mean "crashing into the side of a mountain".

It means "flying normally, into a path that ends on the side of a mountain". That "flying normally" part is really relevant.

well, yes, it also means that.

nothing in that statement implies that crashing was not preceded by normal, controlled flight. the term "crash" has no innate implication besides violent impact. though, yes, in actual use it often implies "accidental" and/or "uncontrolled".

It is a specific term that means the aircraft was flying normally all the way until it reached the ground.

Yes, "crashing on the side of a mountain" is also a correct description of the same event. But those two phrases do not have the same meaning.

Specifically, CFIT is a subset of "crashing into a mountain" where the aircraft was under control all the way until terminal lithobraking. It's implied the last part is usually unexpected, otherwise it would be avoided.

See also: lithobraking.