"You would call them werewolves"
Creative Commons AttributionWolf - Credit: Tambako the Jaguar

The Werewolf Legend

According to the old tales, a werewolf is a human who turns into a wolf at full moon. To become a werewolf, one had to be bitten or scratched by one, or be placed under a curse. The werewolf legends are mostly European, although Native American legends do recount men transforming into animals, called shape-shifters.

Twilight Wolves

The wolves in Forks are Native American shape-shifters, not traditional werewolves. In the Twilight universe, the latter do exist and are mentioned later in the series but are never fully introduced.

The Twilight shape-shifters transform in order to protect their area from vampires.  Theirs is a genetic rather than a magical transformation.

Twilight Werewolf Mythology

The Werewolf Page