Are these two styles of C function pointer definition different?

I have caught myself accidentally using two different styles of C function pointer definitions in different places and have decided to write a minimal program to test these differences.

The two styles in question are:

int (comp (int))

and

int (*comp)(int)

I wrote a minimal program that uses both of these styles for the same function pointer, one for the declaration of a function and one for the definition of the same function, to see what the compiler would have to say about it.

Declaration:

int a_or_b (int (*a_fn)(), int (b_fn()), int (*comp)(int));

Definition:

int a_or_b (int (a_fn()), int (*b_fn)(), int (comp(int)))
{
    int out = a_fn ();
    if (comp (out))
        out = b_fn ();
    return out;
}

As you can (hopefully) see, for the first parameter in the declaration I used the style int (*a_fn)(), while in the definition of the function, I used the style int (a_fn ()). I do something similar with the next two arguments.

I speculated that these might be incompatible types, that these styles might be the difference between a pass-by-reference and pass-by-value assignment of the variable, but when I compiled this program the compiler silently and happily compiled it. No errors, no warnings, nothing.

As I've seen very many tutorials advocating for the second style, while I personally prefer the first style for aesthetic purposes, I am interested in what the difference is between these two styles and which is recommended.

Full code example:

#include <stdio.h>

int a ();
int b ();
int a_or_b (int (*a_fn)(), int (b_fn()), int (*comp)(int));

int a ()
{
    return 1;
}

int b ()
{
    return 2;
}

int comparison (int param)
{
    return param;
}

int a_or_b (int (a_fn()), int (*b_fn)(), int (comp(int)))
{
    int out = a_fn ();
    if (comp (out))
        out = b_fn ();
    return out;
}

int main (int argc, char **argv)
{
    printf ("%i\n", a_or_b (a, b, comparison));
    return 0;
}