The code below demonstrates this difference:
#include <iostream>
#include <string>
int main()
{
        char s[] = "ABCD";
        std::string str(s);
        char *p = s;
        while(*p) {
                *p++ = tolower(*p);          // <-- incr after assignment
        }
        std::cout << s << std::endl;
        std::string::iterator it = str.begin(), end = str.end();
        while(it != end) {
                *it++ = tolower(*it);        // <-- incr before assignment ?
        }
        std::cout << str << std::endl;
        return 0;
}
it produces output:
abcd
bcd
if we separate assignment operation and increment operator:
while(it != end) {
  *it = tolower(*it);        // <-- incr before assignment ?
  it++;
}
the output will be as expected.
What's wrong with the original code?
$ g++ --version
g++ (GCC) 3.4.4 (cygming special, gdc 0.12, using dmd 0.125)
Copyright (C) 2004 Free Software Foundation, Inc.
                The problem is that the order of evaluation of arguments of operator= is unspecified. This is according to C++ Standard 5.2.2/8. Consider the following:
*it++ = tolower(*it);
is equal to
operator=( *it++, tolower(*it) );
Now *it++ could be computed before tolower(*it) and vice versa.
*it++ = tolower(*it); 
*p++ = tolower(*p);
Both of these lines invoke undefined behaviour. You cannot modify the value of a variable more than once in a single statement (++ modifies once, operator = modifies twice).
So the fact that you get different values is unsurprising.
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