Good question! A recent 12 hour delay in Houston had me asking just that. Our flight was scheduled to leave at 9:30 pm, however after waiting for nearly two hours after the scheduled departure time to board we were notified that we would not be flying until the next morning at 9:15 am.
According to the FAA, a flight delay is anything beyond 15 minutes from the schedule departure time. A cancellation is when the flight does not operate at all.
In our case the flight was rescheduled and was assigned the same flight number so it was not considered a cancellation but a delay. The reason for the delay noted was a computer issue with the airplane.
The airline provided all passengers a voucher for a hotel room at a nearby hotel and $30.00 in food vouchers for breakfast at the airport the next morning. Although quite an inconvenience it was reassuring t hat were were not flying on plane that may have had safety issues.