Domestic flights: No immigration / no customs
International flts: Immigration & customs
That's the easy bit!
BFS: Police retain the right to see these passengers but customs not interested (as it is a domstic sector)
Ireland: There is currently a dispensation between UK & Ireland so only a police check rather than full passport check. However it is international so customs may take an interest.
Channel Isles & IOM: No passport check (crown dependancy I think is the term) but not part of UK hence possible customs interest.
It's not easy to get your head round - I know handling agent staff who still have to check before they go & meet some of these flights after a considerable number of years in the job!