To me, Nora just seems a lot more…smart in this version of the play. At least, it’s made much more clearer by the end of Act I that all of her actions thus far have been because she wants to pay off these debts. She’s very good at lying to Terry, as we can see as she lies straight to his face and he sees right through it. But it’s not just to please Terry, it’s so that she can safely and securely pay off this debt on her own time. There is a lot less name-calling (no ‘sqiurrel,’ ‘songbird’, etc.), and generally less fluff, compared to how Nora was constantly trying to put across how perfect their relationship is in the original play. Her role in the household is still traditional, since Terry makes the money and Nora is subservient/dependent to him, but she is certainly not his pet or plaything, which is exactly how Torvald treats Nora in Ibsen’s version. Terry seems to respect Nora for his wife, that is, something closer to an equal and not just another child.
Another thing I found very interesting for Nora is when she discusses with Kristine about how she wants to be more creative, and how she read the book The Artist’s Way. She clearly has ambition and that gives Nora’s character much more depth in this adaptation as opposed to the original play. She has ideas and dreams outside of just her husband and her family, but they seem rather repressed since she writes them off rather casually, mentioning how Dr. Peter called it “bullshit stay-at-home-mom stuff.” Perhaps Gilman emphasizes this so that Nora has more background, and also a valid dream to follow when she goes off on her own at the conclusion of the play.
I would say this is a different character because of these reasons. Both Noras have the same basic personality traits and motivations, but these extra subtleties cause Gilman’s Nora to be more complex, more ambitious and not just a naive little plaything for her husband.