Anne Rice's "The Vampire Chronicles" and Stephenie Meyers "The Twilight Saga", anyone notice this?

Okay so I've read both series as a class project in the last two months and to be honest, I FAVOR ANNE RICE'S Vampire novels more than Stephenie Meyers Twilight series. But I want to know if anyone noticed these smiliarities within Stephenie Meyers work, or you can call it copying. For one, In Interview with the Vampire/Vampire Chronicles there is a coven called "Theatre Des Vampires" who hold a lot of authority over the Vampire world, and then there's "The Volturi" in The Twilight Saga--both covens share a lot in common, thought I believe Stephenie Meyer copied Anne Rice. But that's just one of many things I noticed in Stephenie Meyers work---all of it, except the whole "sparkling in the sun" and a vampire going to high school, came from Anne Rice's the Vampire Chronicles. Even some of Stephenie Meyers Characters share some of Anne Rice's vampire names such as Laurent, Felix, Santiago, and a few more. And if anyone knows who Cauis is, from the Volturi, he shares the same upbringing as Anne Rice's main character Lestat, they both have been involved in a fight with werewolves and nearly died as a result....There is so mcuh more I'd like to state but my main question to you guys is: Do you guys think Stephenie Meyer copied Anne Rice? Do you think she lied about NOT reseraching vampire mythology and fiction before writing the twilight series?