Most CROs have a fixed-gain or CAL position on each input channel sensitivity control. An internal calibration potentiometer can tweak the CAL position to produce a specific sensitivity, such as 20 mV per division. Many CROs provide a square wave signal to check the CAL position sensitivity, but that too needs calibration (infrequently) by an instrument calibration service.
Compensating a probe applies only to probes that provide attenuation of the input signal, typically 10X and 100X attenuation. Compensation is not the same as calibration. Compensation (or frequency compensation) is a capacitor adjustment that allows the probe to pass a band of frequencies without appreciable attenuation discrepancies as a function of frequency. You make the adjustment by connecting the probe to a fast rise-time square-wave signal source, adjusting the compensation capacitor for maximal flatness of the waveform, neither over-shoot nor rounding the edges of the pulses. There usually is no attenuation calibration adjustment. You can determine the actual probe and CRO sensitivity if you have a square-wave pulse generator whose peak-to-peak amplitude is accurately known.