Introverted extrovert= whatever type I am. Extroverted introvert= whatever type those other people are who talk a whole bunch but need some quiet time afterwards
I prefer the term
ambivert for me, and all it means is that I'm a confusing and indecisive person
But really... imagine that you are much more quiet and antisocial than the extraverted side of your type, and much more excitement-seeking and desiring of attention than the introverted side of your type... it's kind of tempting to just say that you're in the middle.
Then you get to the question of "just where do you get your energy?" "Ummm, externally, I think. But the external world sometimes annoys me. And where does Internet interaction fall into this?"
Then you start getting into functions. "If your ego orientation is extroverted, then you are an extrovert by type." "But then extraverted intuition can seem more introverted because it's directed toward the outer world but conceptually." "But then ENxPs are so often defined by being very excitable and talkative... there's gotta be more than this."
It's a big, big mess. And we're all on a spectrum. An introverted extravert would be in the middle of the spectrum and define oneself overall as a extravert by type but with a lot of stereotypical introverted tendencies. This is most common for ENxPs. An extraverted introvert would be the in the same middle but define oneself overall as an introvert by type but with a lot of stereotypically extraverted tendencies. I think I've seen this identification sometimes with ISFx's.
But this isn't a final verdict or anything, just a couple things I've picked up