Not really. They’re not the same thing at all. Being able to be vulnerable doesn’t mean you can handle rejection when it comes. Maybe you can. Maybe you can’t.
Being the cool girl is a defense mechanism in many cases, a way to handle the rejection from being vulnerable. That’s not really handling it well at all, is it? It’s an emotional shut down into a form of apathy so you don’t get burned again. It’s lowering expectations. It’s half in, not a full investment. It’s a wall of separation because you’ve already learned you can’t depend on them. And more often than not, not without reason. We’ve all been the cool girl. Many of us visit the cool girl persona multiple times in our lives.
Thing is, growing past it and learning to be vulnerable again does not guarantee that your needs will magically be met if you communicate them. You’ll still be facing beating your head into a wall to exhaustion most of the time to get the slightest bit of attention and supportive care. They may get it, eventually, long after they’ve done a lot of damage. Or, they may get angry, gaslight, and rake you over the emotional coals for being “crazy".
It’s a coin toss really. At least as the cool girl, you get left alone until you decide to give vulnerablity another try. If it fails, you can always rest your psyche for a while as a cool girl once again.