I rather think that the best description of the difference is how you charge your batteries. An introvert prefers alone time to recharge and an extrovert prefers the company of other people to do the same. A social gathering with many people would drain an introvert and invigorate an extrovert. It has nothing to do with inner tension or peace.
I have seen Susan Cain in the book Quiet talk about introverts as highly sensitive, in the sense that they take in and process more information about the environment. An extrovert would love talking to their friends at a noisy bar, while the introvert would be bothered by the noise and prefer a calmer setting. Being alone is then a way of reducing sensory input to produce a sense of calm, it's not that an introvert would need to be alone to relieve any inner tension.