The extern var declaration in the H vs * only * file defining it in the C file

Question

So, I worked a little with the keyword externto better understand what it does.

I have, for example, the following files:

one.h

#ifndef ONE_H
#define ONE_H

extern unsigned global_var;

#endif

one.c

#include "one.h"

unsigned global_var = 10;

two.h

#ifndef TWO_H
#define TWO_H

void print();

#endif

two.c

#include "one.h"
#include "two.h"
#include <stdio.h>

void print() {
  frprintf(stdout, "%u\n", global_var);
}

main.c

#include "two.h"

int main() {
  print();
  return 0;
}

This compiles fine and produces: 10. As expected.

Now if i change

one.h

#ifndef ONE_H
#define ONE_H

// extern unsigned global_var;

#endif

to be essentially empty, and

two.c

#include "one.h"
#include "two.h"
#include <stdio.h>

void print() {
  extern unsigned global_var;
  frprintf(stdout, "%u\n", global_var);
}

the behavior is exactly the same. That is, my program is still compiling without warnings and exits: 10.

So my question is: what exactly is the difference when creating a global variable anyway? Is one right and the other is not?

Thank,

PS. This has been compiled using gcc -Wallif necessary.