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I'm hesitant to make any conclusive statements about a subject I've never really interacted with (that being Psychology), but just based on what you've said, it seems that there are few ways of characterising introversion and extroversion.
One way is to define them by how others observe someone, as either "shy" or "confident" for example. This is obviously a gross oversimplification, and I'm sure there are more precise words that can be used that capture the nuances of what we think introversion and extroversion should mean.
Another seems to be characterised by personal experience. So, someone is introverted if they themselves feel that they "gain energy" from being alone, or something like that. Please let me know if I'm wrong...
How we therefore describe people on the introverted-extroverted 'spectrum' obviously depends on the definition we adopt. To me, it seems a lot easier to use the second definition as it only has one degree of freedom, and then show correlations between "shyness" and "introversion", and "confidence" and "extroversion". This construction makes the most sense to me since I too personally believe that someone who I perceive as "introverted" need not be shy for example.
Argh I don't know. I probably made this more complicated than it needs to be lol