In my humble experience -- I'm an introvert -- the essence of introversion and extroversion isn't necessarily how you act out socially.
For example, I'm sometimes very extroverted and sometimes very introverted, and often something between. And that's me, so I'm not pretending to be anything else.
However, the key question, it seems to me, is that introverts eventually lose more energy than they gain while interacting with other people. Then they have to recharge themselves alone. Extroverted people seems to gain energy from social interactions, and eventually lose more of it when they're left alone. Again, they can enjoy solitude but it drains them.
Both can do both but an introvert being extroverted or an extrovert being introverted isn't sustainable in the long run.
I would say online interactions consume energy, too. Not on the same imminent level as in-real-life interactions but they do.
Generally if I don't feel like going online to "see" my friends I generally don't feel like going out to see them either. Sometimes I might chat with someone when I wouldn't do that physically but often the said discussion is then less connecting and more shallow.
For example, I'm sometimes very extroverted and sometimes very introverted, and often something between. And that's me, so I'm not pretending to be anything else.
However, the key question, it seems to me, is that introverts eventually lose more energy than they gain while interacting with other people. Then they have to recharge themselves alone. Extroverted people seems to gain energy from social interactions, and eventually lose more of it when they're left alone. Again, they can enjoy solitude but it drains them.
Both can do both but an introvert being extroverted or an extrovert being introverted isn't sustainable in the long run.