Can't take that club guy who looks like a girl seriously.
That's not being introverted. It's being asocial and maybe even towards antisocial.
but not all introverts are introverted to that extreme, and some people are also roughly half and half.
Yeah, those are usually called ambiverts. And there are different levels of those two, since some are very evenly in the middle, while others can reach closer to the extremes on both sides.
The most common misconception I hear is that introverts are bad at social interaction. While that might certainly be the case, it's nothing like any kind of definition. A lot of introverts can be good at it, even if it's not what they prefer all the time.
Typically this results in characters who're desperate for even the slightest bit of social interaction being presented as introverted because they can't manage to interact with others. That's just being an extrovert who's bad at interacting. An introvert wouldn't be that desperate for it.