Katelyn's Mom: The definition of "introvert" and "extrovert" that makes the most sense to me is the one that talks about it in terms of how you recharge your batteries. The introvert is recharged by alone time and is drained by time with people; the extrovert is energized by time with people and is drained by time alone.
If DS4, my extrovert, has more than a few minutes to himself--even if he had plenty of sleep all week--he falls asleep. It just wears him out to be alone. He can actually be quite shy. But he CRAVES social time.
Now, DS7 and I are very social, outgoing and talkative with people, but we both get worn out when with people for long. No one can ever believe that I'm an introvert because I can talk to anyone about anything, and I enjoy it. But it wears me out. I'll have a great time at a party, but then it will take a day's worth of time to myself for me to recover. I'm utterly fine at the party; it's the next day that is a problem because if I don't get the time alone that I need, I get more and more grouchy until I DO get it. It's a need for me, not a want.
DH looks more like the stereotypical introvert than DS7 and I do: quiet, not outgoing. But I tend to be more worn out by social events than he is, and thus score higher for introversion on the Meyers-Briggs Index than he does, even though I don't look like an introvert to most people.
All people need both some social time and some time alone, but the balance is different for introverts and extroverts. And it's entirely possible to be an outgoing introvert or a shy extrovert.
So by this definition, your tight-lipped daughter is an extrovert if she needs social time in order to feel energized. If she's talkative at home but craves her alone time to feel herself again, then she's an introvert.
Does that make sense? I'm not sure I explained that very well...