What makes a hospital a trauma center?

Same. Standards may be the same. The level of care may different, depending on procedures done, and level of expertise available. There are levels1-3, depending on the specialties available/how often are they available.
Multidisciplines. A hospital that is a trauma center makes a commitment to care for the trauma patient from the initial presentation until discharge. Usually has multiple different kinds of doctors including er docs, trauma surgeons, orthopedic surgeons and neurosurgeons. The higher the level of trauma center (1 is the highest), the more complex of patient can be handled.