Here is the BSD implementation:
int
strcmp(s1, s2)
register const char *s1, *s2;
{
while (*s1 == *s2++)
if (*s1++ == 0)
return (0);
return (*(const unsigned char *)s1 - *(const unsigned char *)(s2 - 1));
}
Once there is a mismatch between two characters, it just returns the difference between those two characters.