They're not the same!
It seems that the term "issue" or "issues" has become a fashionable substitute for the word "problem" or "problems". I hear it all the time. Most often when a sports commentator is talking about some player's injury. They always say that the player has a "shoulder issue" — or "issue" with some other part of the body. WRONG!
The player has a physical PROBLEM. The only "issue" is how to deal with it…how to solve the PROBLEM.