Difference between Incident and Problem

This piece of information I took from http://www.devopsmastery.com/devops/2014/2/10/whats-the-difference-between-an-incident-and-a-problem

An incident as defined by ITIL is as follows: "An unplanned interruption to an IT Service or a reduction in the Quality of an IT Service. Failure of a Configuration Item that has not yet impacted Service is also an Incident. For example Failure of one disk from a mirror set." A configuration item is just about anything in ITIL Terms.  Everything from a NIC or Hard Drive to a Web Service can be declared a Configuration Item. It's just something to tie incidents and problems to.

A problem as defined by ITIL is as follows: "A cause of one or more Incidents. The cause is not usually known at the time a Problem Record is created, and the Problem Management Process is responsible for further investigation."

Here are some other quick hit differences:
Problems should be traced down to a root-cause level where as incidents should be resolved as quickly as possible to restore the service to operation.

Incidents like a known issue with a Java application memory leak need become a Problem when they repeatedly occur.  

Incidents can generally be resolved by the person doing the work.

Problems must be closed by a manager assigned in the problem management process.