Precisely. I like the introvert/extrovert description of recharges alone/recharges with other people. I grew up as a serious introvert, but my parents knew the value of social skills. One day my father turned it from a chore into an introvert-style learning exercise by framing it as a skill to be learned and not a quality to be had.
I joined the orchestra, got comfortable with public speaking, learned how to make small talk. I'm not a natural at it, but get by fine today, even in very public sales and lecture/teaching roles.
I still like to go home at the end of a day and recharge alone, but I can use it like a skill and it's been incredibly valuable.