Firefighter drivers and operators are the same thing. "Operator" is the correct term for most emergency fire apparatus, as there are many responsibilities an operator carries in addition to driving the vehicle (such as pumping water, anchoring the vehicle for operating a ladder, being attentive and communicating with their crew, etc.).
Depending on your state and type of department (volunteer or full-time), firefighter driver training and certification can take up to 1 year to complete. Find out what training your state requires by selecting your state.