Under EASA, a single pilot aeroplane, which I assume we are discussing here, has only one commander.
That statement is equally true for single-pilot aeroplanes operated under US regulations.
If it is an instructional flight the instructor is P1 and the student is Pu/t.
The US regulations retain the basic principle of the instructor
acting as PIC, and by the first statement he is the only acting PIC; the difference is that, under the conditions given in 14 CFR 61.51, the instructed may sometimes
log PIC but this logged time is considered as Pu/t (dual) by EASA. An instructed person cannot claim PIC under EASA because US precedent deems the instructor to have been
acting as PIC (cf Admin v Hamre, etc).
As far as I am aware EASA do not recognise the term safety pilot, only an instructor or examiner can also log the time as P1, another pilot going along to keep a look out is a passenger.
The fact that the acting pilot-in-command is styled as a
safety pilot under US regulations should have no bearing on EASA's recognition. It is immaterial that EASA has not established equivalent regulations because, as far as EU regulations are concerned, the
safety pilot acting as pilot-in-command assumed exactly the same responsibilities and duties as are required of a pilot-in-command under EU regulation. That is the test for logging PIC under EASA rules, is it not?