I view Jean/PF/Maddie as different entities.
Jean had a life independent of the PF manifesting. Likewise the PF had a life independent of Jean. These two independent lives merged in some sense but that merged entity is still separate and distinct from the 2 entities that existed before the merger because the combination of Jean and PF results in a commingling of their separate experiences in a way that creates a new consciousness or mentality.
Likewise, while Maddy may have Jean's memories and elements of the PF, she also has memories from Sinister that neither Jean or the PF had. Those memories along with her experiences are unique to her and ultimately help her make decisions and create a life that is separate from both Jean and PF.
In short, while all 3 may share the same template initially, the way that template interacts with the world and the other disparate elements of each individual results in each incarnation of PF/Jean/Maddy being distinctly different from the other.