Originally Posted by schrödinger's cat
This is interesting. I'll give this a shot. Some attempted definitions of extraverted introverts and introverted extraverts...
Gregarious introverts: Love parties and hanging out with people. Sounds extraverted? It isn't really. They'll usually talk to a limited number of people, or they'll hang out with their closest friend(s). They don't really interact with the whole group. And they'll often focus on doing stuff like playing a game, dancing, building the fire for a BBQ... which takes off the "social pressure" a bit. Are often content to just watch the action. If life were a band, they'd be the drummers and bass players.
Reserved extraverts: Love parties and hanging out with people, but for them the experience is so intense that they need time alone afterwards: not in order to regain energy (as an introvert would), but to process their thoughts. Some focus so intensely on people and interactions etc. that they later have to spend some time to get into their own skin again, to "feel themselves" and re-focus on their own view of the world. Plus, while they're with people they're aware of so much information that they later need some time to process it all.
Not-all-that-gregarious extraverts: Focus on the external world and take their energy from it. Classical extraversion. But "external world" does not equal "social interactions". People stuff is exhausting to them, perhaps even pointless. What they focus on could be stuff like organizing a project or discovering new stuff (cities, cars, museums, machines...). When with people, they'll prefer talking about matter-of-fact topics (modern art, or new cars, or the latest project they're doing, or politics, or the news), and they'll try and keep the discussion as matter-of-fact and as un-subjective as they can.
That's all I can think of for now. Perhaps there are more.