An interesting heuristic difference between the two types of, lets call it, challenges, is how you define success. In a puzzle, you achieve success as a well d

An interesting heuristic difference between the two types of, lets call it, challenges, is how you define success. In a puzzle, you achieve success as a well defined solution, or (in a lot of the theoretical cases) by showing no such solution exists. In a problem, there is many goals to balance (simplicity, efficiency, cost, implementation time, etc). Often, the best solution is not needed, or the "optimal" one is too complex or takes too long to implement. Often, the perfect solution is not possible, and you have to think about how to change the definition of the problem to get something acceptable.