Interchanging two variable values using pointers in C doesn't work

For the second approach, you need to pass the pointer to pointer to an integer. You will also need to define pointers to your integer variables (as you will exchange the references and you need objects which will hold the references) It will not exchange values of your integers.

To modify the object passes to the function you need pass the reference to it (pointer).

void interchange_values(int **first_number_pointer, int **second_number_pointer) {
   
    int *temporal_variable;

    temporal_variable = *first_number_pointer;
    *first_number_pointer = *second_number_pointer;
    *second_number_pointer = temporal_variable;

};
int main(void)
{
    int a = 5; int b = 10;
    int *pa = &a; int *pb = &b;

    printf("Before: a = %d b = %d\n", a , b);
    printf("Before: *pa = %d *pb = %d\n", *pa , *pb);
    interchange_values(&pa, &pb);
    printf("After:a = %d b = %d\n", a , b);
    printf("After: *pa = %d *pb = %d\n", *pa , *pb);
}

Result:

Before: a = 5 b = 10
Before: *pa = 5 *pb = 10
After:a = 5 b = 10
After: *pa = 10 *pb = 5

https://godbolt.org/z/vfrfzK1r9

In the first example you are passing the variables for the desired change by reference (via pointer).

The pointers themselves are passed by value which, as others have mentioned, means that their scope is local to that function.

This is why in the C standard library you see functions that accept pointer pointers when there is a need to potentially change not only the base data but also potentially the pointer itself. An example of such a function would be the root of trees included in search.h. Any function that could reallocate memory and physically relocate the root in memory accepts a pointer pointer, because you pass the pointer by reference. tsearch might need to move the root, so it accepts a pointer by reference, while twalk wouldn't ever modify the root so it accepts the pointer by value. Link to man page for the described tree functions

Edit: Simple Example

#include <stdio.h>
#include <stdlib.h>

void interchange_pointers_by_reference(int ** first, int ** second)
{
    int * tmp_ptr = *first;
    *first = *second;
    *second = tmp_ptr;
}

int main()
{
    int * foo = malloc(sizeof(*foo));
    int * bar = malloc(sizeof(*bar));
    *foo = 1;
    *bar = 2;
    printf("foo = %d, bar = %d\n", *foo, *bar);
    printf("running function\n");
    interchange_pointers_by_reference(&foo, &bar);
    printf("foo = %d, bar = %d\n", *foo, *bar);
    return 0;
}

scott@scott-G3:~/tmp$ gcc -o example example.c
scott@scott-G3:~/tmp$ ./example 
foo = 1, bar = 2
running function
foo = 2, bar = 1