- My View
I would recommend you read through the different docs on the subjects. Here's the link to ITSM for Jakarta. There are also tons of articles online regarding ITIL.
A real example could be an employee reports an incident. Their incident (issue) is they cannot log into an application supported by your company. The appropriate support team would work to resolve the incident. If a root cause is needed to determine why the issue occurred and prevent future recurrences, a problem can be opened. A problem could also be opened for known workarounds. In simple terms, I like to think of Incidents as an issue that disrupts or prevents users from doing their normal job duties or interrupts a system/service. Problem is the cause of the Incident(s).