"issue matter, and problem"
They can often be used synonymously, but can also mean different things.
- problem - a difficult question, matter or situation that has to be solved for good outcome.
- matter - a thing or situation that deserves attention and needs to be addressed. May or may not be a problem per se.
- issue - a problematic matter.
* "problem" may be technical ("engineering problem") or non-technical; "issue" is always sociopolitical or organizational.
Here are cases where they are not interchangeable:
- a math problem. (there is no such thing as "math issue" or "math matter").
- The election is a matter of great importance. (However, it is not necessarily a problem or an issue)
- The incident implicates a human rights issue. ("problem" doesn't fit as well)