This has been a meaningful distinction since at least C99.
> "a pointer to an array of X" is simply "a pointer to X"
They aren't actually the same. The former can be decayed into the latter but they aren't actually equivalent and you'll get type mismatches if you try to treat them as the same thing.
> who has families of functions with the same type signatures that they want to point to
An example is callbacks or handlers for responding to interrupt requests. A lot of hardware interface code relies on typedef-ed function decls because very often you are passing user side functions through your interface so that you can stash those function pointers somewhere and invoke them when some event occurs.
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