Math question: Is a vampire still a vampire if he 1) no longer feeds on humans, 2) is no longer killed by sunlight, 3) cannot shapeshift into any desired form, be it animal or swollen fog, 4) can still bite someone and not necessarily turn them into a vampire?
Twilight asks this question without ever asking it directly. It presents the term 'vampire' as a vague representation, a blanket that can cover whatever it wants, some of which are sexual aspects popularized by Anne Rice, others that are inventions of the author probably due to some unresolved and improperly tended fetishes.
In any art form, it is not a requirement for the material to conform to the formulas set by previous works. Isabella Swan, the main character played by Kristen Stewart who is for once not being terrorized in a house, arrives at a new school in the Pacific Northwest, pale, bulemic and smack dab in the middle of a painful 3-parent situation (how tragic). In spite of being crippled by what could be an obvious dramatic device, she has no problem making friends or attracting members of the opposite sex. She isn't bullied by teachers or her fellow students. Her father is the soulful, quiet chief of police, the furthest thing from an asshole or a creep. He buys Bella a truck and mostly leaves her alone, only attempting once or twice to connect with her.
Bella's first meeting with Edward (equally pale) is watching him rush out of class after she steps in front of a revolving fan. Other than this, there is no obvious indication that vampires are about to occur. The slow buildup to the revelation of a larger world underneath the normal one is actually (and surprisingly) well done. A rational, non-supernatural explanation is offered for every strange thing that Bella sees about and around Edward until he saves her from being crushed by a van. Then, it is only inevitable that she finds out: he is one of them 'pires.
It pretty much goes downhill from there.
Edward has heightened senses, super strength/speed, and a thirst for blood (which he sates by feeding on animals, calling the practice "vegetarian"). He sparkles in the sunlight like a Christmas ornament, but cannot shapeshift. He controls his filthy vampire urges enough to keep from biting his classmates. For fun, he plays vampire baseball with his family set to the inappropriate tune of Supermassive Black Hole by Muse.
It is exactly as stupid as it sounds.
Other than struggling with this relationship that is a poorly-concieved metaphor for relationships IN THE REAL WORLD, Bella spends much of her time fitting into her new life in the Pacific Northwest, which is still the most interesting part of the film but which is now a flaw due to the bullshit surrounding Edward, his family, and the arrival of some one-dimensional neck-feeders. When shit hits the fan and the third act kicks in, it is abrupt, awkward, and resolved in ten minutes. Then a couple of more scenes happen and the movie finally ends with a criminal misuse of Radiohead's 15 Step.
There is also promise of werewolves at some point, because the marriage of those two has always worked out so incredibly well.
The math equation above is a simple one to solve, like when the CDC suddenly discovered that zombies can run. The question is no longer "Is a vampire still a vampire?" but "Is a vampire still interesting?"