Another way I like to describe the difference between introverts and extroverts is that introverts are energised by solitude, while extroverts are energised by company. Introverts certainly want to socialise as much as extroverts, but they then need to retreat to recharge, while an extrovert will find alone time draining, and need to retreat to a social setting to recharge.
Great way to sum it up, by that measure I'm a clear introvert. That doesn't mean shy, quiet in gatherings or even unhappy in company of others, but group time is exhausting and alone time is, as you say, recharge time.
