CFI: Chief Flying Instructor - within an organisation, not a CAA rating.
FI: Flying Instructor
FI(R): Flying Instructor (Restricted) - on initial qualification as FI you are not allowed to send students first solo or first solo cross country. This restriction is lifted after gaining experience under the supervision of more experienced instructors.
AFI: Assistant Flying Instructor - pre-JAA equivalent of FI(R), no longer in use.
QFI: Qualified Flying Instructor - military only rating (in UK) meaning an instructor who has passed an RAF Central Flying School course in flying instruction.