This is exactly the kind of made up division I'm talking about. There is no such thing as "someone who 'emotionally recharges X or Y way'".

First of all: Why exactly would Wikipedia - edited by thousands - be wrong if the way you put is "what they are defined as"? Wouldn't people have written Wikipedia that way then?

Next, there is no such thing as "emotionally recharge". Our "emotions" aren't a battery. Also, there is "recharging process" or anything. Generally speaking: Activities that make us happy in that very moment "recharge" our batteries. Parents of young children will confirm that this not neccessarily a task that gives you respite, but can be the most exhausting thing ever, still you'll come out of it with more energy than before.

And we all - everyone! Yes, you too! - have varying ways of doing that. Sometimes, we'll want to be around others and it'll do us good, sometimes we want to be alone and it'll do us good. While all people will have tendencies towards one way or another, no one has a defined "recharging mode". No one.

And lastly: The main issue with this division into "introverts" and "extroverts" is not that it's impossible to divide people by that line. You can, as you can with many, many other lines one could draw. The issue is that people offhandedly attribute all kinds of stuff to this division. All of a sudden, extroverts are "loud" and "confident" and "energetic" and "sports guys". Even IF we applied your definition... how would the way someone wants to take a break in lead to them being even one of those things? It's just not logical.