According to Carl Jung, who invented the terms introvert and extrovert, the two are really about preferring to focus inside or outside yourself. They don't necessarily have a social connotation.

The introvert, according to Jung, generally perfers to focus on his own feelings, thoughts, ideas, dreams.

While the extrovert, generally prefers to focus on things outside himself, like objects, other people, and their ideas, feelings, etc.

So, in the original sense, these definitions have absolutely nothing to do with shyness or lack thereof, or about feeling "drained" by interaction with people vs being alone.

An introvert could be perfectly happy being with other people, as long as he can focus on his own internal world. And an extrovert could be happy being alone, but as long as he can focus on people or things outside himself.