POB is exactly that = people on board.
It is more for SAR than anything else that the figure is included. Heavens above in the unlikely event of an accident, the emergency services are looking for a total amount, not x crew and y passengers.
That can be sorted out later.
As to souls on board, I think that is some casual non-ICAO term that was used by someone and everyone else thought it was good and fancy to use, so they all use it now.