Instructor ratings are listed in JAR-FCL 1.305 and are divided into categories: (A) = Aeroplane
FI(A) Flight Instructor
TRI(A) Type Rating Instructor
CRI(A) Class Rating Instructor
IRI (A) Instrument Rating Instructor
SFI (A) Synthetic Flight Instructor
Each category represents a different rating, all of which can stand alone or in some cases can be combined.
JAR-FCL 1.330
The FI(A) starts of as a FI(Restricted) and on removal of the restriction becomes a FI(A) the unrestricted rating.
additional privileges can be added to the FI rating:
Applied IF, equivalent to IRI with different entry requirements for IMC training.
Class Rating Multi Engine, entry requiremens similar to CRI.
Aerobatics
Flight Instructor Course (FIC) Instructor.
There are some anomalies in that the UK national system used to apply "limitations" to the basic FI rating, whereas the JAA system adds privileges to the basic FI rating. The CAA computer is still programmed with the old system!
If you are a FI, you don't need to become a CRI or IRI as these are included in extensions to the FI privileges. An IRI or CRI is a stand alone qualification with limited privileges.
There is no Examiner Rating; it is an Authorisation.