Difference between string and char[] types in C++

I know a little C and now I'm taking a look at C++. I'm used to char arrays for dealing with C strings, but while I look at C++ code I see there are examples using both string type and char arrays:

#include <iostream>
#include <string>
using namespace std;

int main () {
  string mystr;
  cout << "What's your name? ";
  getline (cin, mystr);
  cout << "Hello " << mystr << ".\n";
  cout << "What is your favorite team? ";
  getline (cin, mystr);
  cout << "I like " << mystr << " too!\n";
  return 0;
}

and

#include <iostream>
using namespace std;

int main () {
  char name[256], title[256];

  cout << "Enter your name: ";
  cin.getline (name,256);

  cout << "Enter your favourite movie: ";
  cin.getline (title,256);

  cout << name << "'s favourite movie is " << title;

  return 0;
}

(both examples from http://www.cplusplus.com)

I suppose this is a widely asked and answered (obvious?) question, but it would be nice if someone could tell me what's exactly the difference between that two ways for dealing with strings in C++ (performance, API integration, the way each one is better, ...).

Thank you.