Can I use a Belfast on-street parking ticket in a city council off-street car park?

No.

An on-street paid session is for the street location it covers, while a council off-street car park is a different parking place with its own tariff and enforcement arrangements. In Belfast this matters because both types can be close together in the city centre. If you leave a street bay and move into a council car park, start the correct parking session for that site rather than assuming the time already bought follows your registration number. Always check the displayed location code.