To answer the original question - EASA and the FAA define "Pilot In Command" differently. In FAA-land there are, for example, a number of cases where you could be flying with an Instructor and receiving tuition and log the time as "PIC". You can also log "PIC" time if acting as a safety pilot for someone who is flying using a view-limiting device who is also be logging the time as "PIC".
In EASA-land only one person at a time can log time as Pilot In Command in an aircraft certified for single-pilot operation (with a few exceptions which you are unlikely to run in to while training) - so if you are flying with an Instructor the time would be "Dual" or "Pu/t" rather than "P1".
Under EASA rules you don't have to be solo to log P1 /PIC time, you can carry a passenger. What you can't do is carry an instructor and receive training, or have another pilot on board who is also logging P1 / PIC time.
When I did my FAA training I got a private certificate first, and then most of the hours I did for my IR training counted as PIC time towards the minima for the Commercial. I'm currently hour-building to meet the EASA P1/PIC CPL minima.
If you have passed the FAA written and oral exams you will find the EASA exams a lot easier than someone starting from scratch, but there is a lot more information to take in and much of it is of very little practical value. I found the EASA exams very frustrating - I was happy to work hard but I would have much preferred spending the time learning something useful rather than the reams of dross obscuring the occasional pearl of wisdom. I spent many unhappy hours learning about the Microwave Landing System (MLS) - that well known approach aid found at so many international airports .....