This is a good thing!
There are billions of people, each with their own unique
experiences, and it is impossible to account for all of the ways
in which some of those people are plural. There are too many
factors, and the idea of a singular state of self is merely an
assumption.
There are ways of becoming plural that are nonvoluntary and
others that are voluntary. Plurality can be spiritual,
psychological, neurological, natural, metaphysical, et al.
Source is only one facet of plurality, and it can be important
or trivial. That's up to the plural in question.
Limiting our understanding to a single narrative of plurality is
at odds with respecting the ability of others to define their
own experiences.
Terms such as "plural," "system," and "multiple" belong to all
plurals who want to use them.
Hoarding plural terminology and claiming it's exclusive to a
specific category of plurality is unnecessary gatekeeping that
doesn't benefit anyone, including the people who do the
gatekeeping. It's dishonest and doesn't reflect reality or
history.
Introject is a generic term for any system member who has a
source external to the system.
There are no rules for how an introject identifies with their
source material. introjects can identify "as" their source or
"like" their source or anything else.
A fictive/factive/other introject may keep the same identity as
their source or they may not. Neither of these is superior to
the other.
Insisting that all introjects must feel a certain way about
their source is harmful and prevents their natural development
as living beings.