As there is no agreed upon central authority defining "natural" and "normal" birth, everyone reads into it what they will, and the many definitions create far more confusion that clarity. I prefer the universally understood terms like vaginal vs c/s birth, induced vs spontaneous labor, medicated vs drug-free labor.
Normal can only be defined in context. In our regional medical center with the NICU, epidurals (at 90%) ARE normal and they think natural births include episiotomies and directed pushing. I think it's a VERY small group of women who comprehend intervention free and natural birth.
Another gripe I have with the word "natural" is how the Madison Avenue types have turned it into a buzz word for good and wholesome while radically devoid of any semblance to how things occur in nature. I'm a homeopath and see "homeopathic" used in the same manner with no connection to the practice of homeopathy or to substances prepared according to the standards of the Homeopathic Pharmacopoeia of the United States. Because "natural" has become such an emotionally loaded term, women can interpret it as a slam against their maternal fitness. I think that's one reason so many online discussions about natural birth turn into flame wars... women are reacting to inferred judgments about them rather than responding to an argument.
That's my ramble.