Confusion on how to use strchr in C

char *strchr( const char *s, int c );

I understand that strchr locates the first occurrence of character c in string s. If c is found, a pointer to c in s is returned. Otherwise, a NULL pointer is returned.

So why does below code outputs num to strlen(string) rather than what its designed to do?

num=0;
   while((strchr(string,letter))!=NULL)
   {
      num++;
      string++;
   }

But this code gives correct output

num=0;
   while((string=strchr(string,letter))!=NULL)
   {
      num++;
      string++;
   }

I fail to see why assigning the pointer that's returned to another qualified pointer even makes a difference. I'm only just testing if return value is a NULL pointer or not.

1. string is a pointer.

2. In the first example, you just move it right one position, regardless of where (or if!) "letter" was found.

3. In the second example, every time you find a "letter", you:

   a) update "string" to point to the letter, then

   b) update "string" again to point just past the letter.