A quick overview
As I see it, a differentiated function is not a cognitive process. It's the means by which emotion is integrated with the operations of the executive brain in the conscious decision to take action.
Undifferentiated functions remain allied with the unconscious emotional subsystem, and they're always operating to bring their products to consciousness. But their products may not reach awareness unless they're consonant in some way with the interpretive principles the dominant function has set up.
This is why developing behavioral skills associated with a function is, in general, a positive thing. It broadens the sphere of options that we recognize within the context of our type preference. New solutions to old problems become available to us.
Doing this, however, bears no immediate relationship to "individuation." Rather, it results in ego maturation, an expansion of conscious potential.
Individuation, by contrast, builds a bridge to unconscious aspects of the psyche, by way of art or religion or dreams, aligning ourselves with sources of guidance that the cognitive system can't co-opt on its own terms. This *reduces* our identification with the dominant standpoint's interpretive selectivity, rendering the ego and our functional preferences less important.The Four Functions: Psychological Orientation vs Determinism
To put this somewhat differently, the functions represent four different ways that our unconscious emotional subsystems are brought into relationship with our higher mental operations, moving them into the stream of consciousness. As such, the functions aren't cognitive processes. Rather, they make our emotional energies available to the operations of the executive brain.
By operations of the executive brain, I mean the capacities that make us fully human: the ability to pick out relevant information from what is perceived through the senses; the ability to apply old information to new situations; the ability to initiate behaviors that haven't been learned; the ability to inhibit behaviors to which we are immediately inclined; the ability to form new ideas by linking signs in novel ways; the ability to infer others' intentions; the ability to envision a goal that is not locally apparent.
These aren't "skills" that match up with different functions; they're the cognitive basis on which all functions operate.
When we differentiate a function, we turn it into a consistent cognitive channel for our emotional energies, so that we feel an emotional investment in the discriminations we're making. And we feel in control of our emotional life on that basis, as we inhibit some immediate reactions for the sake of personal or cultural advantage. This is how an accustomed orientation becomes habituated.
My contention, therefore, is that type preference liberates us from instinctual determinism by way of conscious discrimination, whereas Temperament Theory understands preference to confirm an underlying archetypal determinant.
With respect to the latter understanding, it seems to me that most of the monographs in Jung's "Psychological Types" serve to distinguish type theory from the credible temperament theories existing at the time. In each chapter, Jung explores the common ground a popular temperament theory shares with his type theory, then proceeds to show that the apparent kinship is superficial, and that the temperament theory being described is concerned more with affective determinism than with psychological orientation.
Jung points out, in fact, that when temperament moves us to react immediately, without discrimination, we don't congratulate ourselves on being natural and authentic. We're more likely to say that we "weren't ourselves," or momentarily "lost" it. What is it that got lost? Our distinctly human ability to channel or inhibit a natural reaction for the sake of a conscious purpose. This is what we mean when we say we make free-will choices -- we commandeer or block natural tendencies for the sake of an aspiration or a goal.
Jung explicitly says that this is what he wanted to capture with his type theory -- not a way to characterize people by way of innate qualities that can't be controlled, but a way to classify how people make choices they feel free to make, believing that one thing is better than another -- even when it *doesn't* meet their immediate affective needs. The consistency of such free-will choices over time becomes a pattern -- not because it's inborn, but because we become accustomed to interpreting and responding to life in a way that we find satisfying and comfortable.
Jung didn't deny the influence of temperament altogether. He accounted for it, in classic neurobiological terms, by way of the attitudes. Some people, he said, have strong biological constraints with respect to approach and withdrawal, and they can be psychologically harmed if they're forced into choices in conflict with their natural tendencies. On the other hand, he also said that most people are adaptable enough to meet prevailing social expectations, pointing to the general Extraverted attitude of Americans as a good illustration.