What's the difference between extroversion and second-handedness?

According to Wikipedia, extroversion is "the act, state, or habit of being predominantly concerned with and obtaining gratification from what is outside the self." A key distinction between introverts and extroverts is that extroverts mentally "recharge" by interacting with other people, while introverts do that by being alone. Does being an extrovert mean that you're second-handed? Is it a moral failing of any kind?