In my mind your argument is equivalent to to separating novels based on if they were written with a pen or a pencil. Yes, there's a difference between a pen and a pencil, but that has no effective bearing on the novel as written. And it doesn't make sense to categorize novels based on that.

Cfront was Bjarne's original C++ compiler. It translated C++ code into C code which would then be passed through a C compiler.

I didn't think Cfront should be called a compiler, because it didn't compile down to machine code and not even to assembly, only to another relatively high level language.

Bjarne was quite insistent that Cfront really was a compiler, and the fact that it compiled to another source language was immaterial. It did essentially the same things as any compiler, it only had a different back end code generator. And the code generator could later be swapped out for one that generates machine code.

Of course you can call it whatever you want, but Bjarne called it a compiler.