Method for operating a braking system for a motor vehicle and corresponding braking system

A method for operating a braking system for a motor vehicle, wherein the braking system includes a service brake unit and the service brake unit is activated to generate a brake force on a wheel axle of the motor vehicle at least temporarily as a function of a setting of an operating element, wherein the generation of the brake force as a function of the setting of the operating element is performed using a calibration data set stored in a control unit of the braking system, wherein an identifier stored in the operating element is transmitted to the control unit and used there for a compatibility check and, if the compatibility check is successful, a configuration of the operating element takes place in that a generic data set stored in the control unit is used as the calibration data set and an operating element-specific data set stored in the operating element is transmitted to the control unit and used as a calibration data set after the transmission.