While it's probably likely that the two often go hand-in-hand, introversion is not simply another way of describing "social submission." I'm introverted, in the sense that social interactions are tiring for me. But that doesn't mean that I don't enjoy them.
For instance, if I spend all day at a conference talking with people, then I probably don't want to go to a cocktail party that evening. But if I am locked in my office all day writing a brief, then I'll definitely get excited for a happy hour.
Also, I was always pretty popular when I was younger. (There isn't much of a social ladder at my stage of life. I'm married, and my wife and I are both very professionally successful, so I guess that gives us a certain status, but it has nothing to do with being "cool.") I was the captain of a few teams, always had girlfriends, etc. When I was younger, I was always the defacto representative of a group when we needed to deal with adults. Being introverted didn't preclude any of that.
In fact, in some ways I think it helped me. I was very good at having serious one-on-one conversations where I really listened to people (classic introvert trait), and I think that made people like me. Lots of people who weren't among my closest friends felt like I understood and respected them, just because of a random conversation we had one time. I can't count the number of times I would pursue a girl and she would eventually tell me that she had asked people about me, and it would turn out that people who I didn't think I was that close to had told her really good things about me.