All NP complete problems are NP hard problems when solved in a different way.
But, all NP hard problems are not NP complete.
Ex:
1. Traveling salesman problem. It is both NP hard and NP complete. We can find that whether the solution is correct or not in the given period of time. In this way, it is NP complete.
But, to find the shortest path, i.e. optimization of Traveling Salesman problem is NP hard. If there will be changing costs, then every time when the salesperson returns to the source node, then he will be having different shortest path. In this way, it is hard to solve. It cannot be solved in the polynomial time. In this way, it is NP hard problem.
2. Halting problem.
3. Sum of subset problem.