I fit this description too. I consider myself an introvert (that is, more introverted than extroverted; very few people are exclusively one or the other) because I need to be alone to recharge. When my "social battery" is full, I eagerly start conversations with strangers, and even when it is drained I'm comfortable talking to people, though I might not desire to.

I get tired from talking too much with people, and need to rest by being by myself, I guess is the gist of it. Still enjoy it though, like swimming in the sea, tiresome but fun :)

Introvert doesn't mean one doesn't enjoy socializing, just that one needs quiet down time to recharge from it. Extroverts tend to be energized by socialization. It's also not always so cleanly binary, either.

I really hate that introversion gets conflated with social anxiety or misanthropy on the internet.