The biggest difference is that she seems to believe that when she is not around, I don't exist, my life just is frozen in time somehow.
That's because a symptom of BPD is a lack of object constancy, meaning out of sight out of mind, literally for a borderline. Mine once asked me to leave a dirty t-shirt with her, so she could use my 'smell' to connect me to her. You could say it was romantic, but in her case she knew people ceased to exist for her when they weren't with her physically, and she was trying to do something about it, which I give her credit for.
She also thinks that my feelings are tools for her to use to get me to do what she wants.
Yes. BPD is all about need fulfillment, getting needs met, by using another person, and the pain they're in justifies it to them.