Isn't string equals to const char *?

[sawer]

I am reading some documents about c++ and it says:In c++ string is equals to const char *.Is this true?
Because i compile this code:

#include <iostream>
#include <string>
using namespace std;
int main() {
	const char * p="ppppp";
	string s="aaaaaaaa";
	s+="eeeee";
	s=p;
	p=s;//gives error:error C2440: '=' : cannot convert from 'std::string' to 'const char *'	
}

Isn't string equals to const char *?If equals why does this error occur and why does compiler give permission to change value of string s after initializition?