State data in functor members vs global function

Question

When comparing functions and functors, it is often mentioned that one advantage of a functor over a function is that a functor is statefull.

However, in this code, it seems to me that a function may be statefull too. So what I am doing/understanding wrong?

struct Accumulator
{
  int counter = 0;
  int operator()(int i)
  { 
    counter += i; 
    return counter;
  }
};

int Accumulate(int i)
{
  static int counter = 0;
  counter += i;

  return counter;
};

int main()
{
  Accumulator acc;
  std::vector<int> vec{1,2,3,4};
  Accumulator acc2 = std::for_each(vec.begin(), vec.end(), acc);
  int d1 = acc(0); // 0, acc is passed by value
  int d2 = acc2(0); // 10

  std::for_each(vec.begin(), vec.end(), Accumulate);
  int d4 = Accumulate(0); // 10

  return 0;
}

Answer 1

Each instance of a functor has its own state, while the static member of a function would be shared.

If you called for_each multiple times with the Accumulate() method, the counter would never reset, and each subsequent call would begin where the previous call ended. The functor would only have this behavior if each instance was reused. Creating a new functor would solve the problem.