Both systems most are required in car for propose of passenger safety. The Seat Belts are known as Primary Restraint System, which keep your body attached to the seat in case of a sudden acceleration/deceleration. Seat belts are known for saving thousand of lives, they saved people from flying away through windshield in case of high speed accidents.
The Airbags are known as Supplementary Restraint System, which protects an occupant from severe injuries in case of an accident. The purpose of the airbag is to provide the occupants a soft cushioning and restraint during a crash event to prevent any impact or impact-caused injuries between the flailing occupant and the interior of the vehicle.
Source Video: Mazda