Problems have one right answer that can be reached by analyzing the information you have.
Dilemmas don't have one right answer. Any solution will be at least partially wrong, unfair or harmful to some stakeholders. But not making a decision will be harmful to all stakeholders. The challenge is to minimize the damage and, occasionally, to optimize the benefit.
Mysteries are often hidden within too much information. Understanding them is closely aligned to the ideas contained in complexity theory and risk management. Accepting your inability to know the answer to a mystery is critical: Make the best decision based on the limited information available while staying prepared for surprises.
Puzzles can often be resolved through measurement and research. Gather the right information and skills, and you reduce a puzzle to a problem and can then calculate the optimum answer. If there's insufficient time to gather and analyze all of the necessary information, though, you may be forced to deal with the decision as a mystery,
When confronted with a difficult decision, recognize the differences between the types of possible decisions and then use the best approach to reach your conclusion. Many issues around decision making stem from a false hope that we just need a little more information to reduce a complex decision to a problem with just one right answer. Yet in many cases, this is just not possible.
All project managers make decisions. The difference between good project managers and great ones is the percentage of decisions they get right.