What is the difference between an incident and a problem in ITIL 2011?

ITIL Glossary definition extract from Axelos:

Incident : An unplanned interruption to an IT service or reduction in the quality of an IT service

Problem :  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

Important to Note: an incident does not become a problem. Rather, we initiate a problem when we would like to find the fundamental cause of the incident.

So in ITSM solution (like CA ServiceDesk, Remedy...), we create the problem and we link one or multiple incidents to the problem.

When the problem management team find the cause and implement the solution, we close related incidents.