Skill Test, Proficiency Check, Flight with Examiner, Instructor Flight and All Other Types of Checks

The EASA FCL easy access rules document is helpful.
https://www.easa.europa.eu/sites/default/files/dfu/Part-FCL.pdf

Can’t answer all your questions but have one example:
Multi pilot multi engine typerating.
To revalidate it’s required to do one license proficiency check per year. In commercial ops however an additional operator proficiency check is required longest every 6 months. Also once a year a line check is required.
In practice it’s two days of sim (day 1 4h training, day 2 4 hours check) every six months and a line check every 12 months.

Some operators (biz jets) also opt to do the training and checking onboard the aircraft instead of a sim.

Proficiency check: the test to revalidate a currently valid class or type rating (not renew which is when the rating has expired).

From FCL010

“Skill test” means the demonstration of skill for a licence or rating issue, including such oral
examination as may be required.

“Proficiency check” means the demonstration of skill to revalidate or renew ratings, and including
such oral examination as may be required.
“Renewal” (of, e.g. a rating or certificate) means the administrative action taken after a rating or
certificate has lapsed for the purpose of renewing the privileges of the rating or certificate for a
further specified period consequent upon the fulfilment of specified requirements.
“Revalidation” (of, e.g. a rating or certificate) means the administrative action taken within the
period of validity of a rating or certificate which allows the holder to continue to exercise the
privileges of a rating or certificate for a further specified period consequent upon the fulfilment of
specified requirements.

Training flight with instructor: the flight done for revalidation of SEP. This one is used e.g. on FOCA/BAZL form 60.521 (Revalidation Class Rating SEP / TMG). Is it used for anything else?

To meet the requirements of FCL.740A

— refresher training of at least 1 hour of total flight time with a flight instructor (FI)
or a class rating instructor (CRI). Applicants shall be exempted from this refresher
training if they have passed a class or type rating proficiency check, skill test or
assessment of competence in any other class or type of aeroplane.

Examiner flight: a flight done before the actual proficiency check in some cases,

No such thing, its either a Skill Test, Prof Check or Training. A FTO may conduct a practice test but this does not have to be an Examiner

Familiarization flight: not an official term I’ve seen but just adding it here for completeness. This would be the flight you conduct with an FI to get familiarised with a new SEP airplane.

Familiarisation Training, no requirement for a flight, may be reading the FM no requirement for a signature
GM1.FCL.710

Differences Training does however require flight training at the discretion of a Instructor and a signature

Skill test vs. proficiency check:

Initial issue versus revalidation or renewal

Proficiency check vs. line proficiency check:

One revalidates your rating, the other is to meet the 6 monthly requirement for operator proficiency

If you do not have the 10 sectors in the period of validirty of a MEP or Type rating then you must complete one Sector with the Examiner. That is section 3a of the Prof Check and would be completed on the same flight, you do most of it anyway. If you do the IR revalidation Section 3b, on the same flight you are exempt Section 3a

PART. FCL Appendix 9

(d) Section 3A shall be completed to revalidate a type or multi-engine class rating, VFR only, where
the required experience of 10 route sectors within the previous 12 months has not been completed.
Section 3A is not required if section 3B is completed.