Tha answer is in JAR FCL1. Have a look.
Basically, dual is all flying with when receiving instruction under JAR FCL, i.e, base training should be logged as dual, because you are not qualified on the type yet.
Commander, is a pilot nominated by the operator, there can be only one on board. Commander has all the legal responsibilities and power. Commander always logs P1 - PIC, even if he is asleep in the bunk.
Once you have a licence, and you are not a Commander, you log co-pilot time. Co-pilot is any pilot on MPA who is not the commander, even if you have captain licence. This would apply for flights with two captains and for all F/Os
If a captain is receiving any instruction, he would log PIC(Under Supervision) time. He cannot log straight PIC time as this is reserved for commanders only and that will be the instructor (provided he is occupying the right hand seat). But such captain trainee acts as a commander, so he logs what he does - commanders time under supervision.
To gain PIC time for ATPL, F/Os often need some extra PIC time. FCL has a provision to it. Under approved training syllabus F/O can play the commander while being supervised by an instructor. In this case, F/O may log PIC(US) time as well. WARNING: This is JAR FCL rules. UK CAA set a different rules under which F/O logs PIC(US) for legs where he is the pilot FLYING. This is clearly contravention of JAR FCL, but that is how it is done.
FD
(the un-real)