dBm is the power level in dB referenced to 1 milliwatt. It is an absolute quantity that can be computed from Watt for instance.
dBc stands for decibels relative to carrier. It is a relative quantity and used to indicate the level of spurious signals relative to a main input signal. Use this calculate to input two signals (in dBm) and calculate the relative level in (dBc)
dBc = dBmsignal – dBmspur
The following phase noise plot shows spur levels relative to the carrier. A dedicated phase noise tester will typically detect the carrier and make the computation automatically.
If this measurement is performed on a general purpose spectrum analyzer, the user has to apply markers in the user interface to determine the dBc value. In both cases the computation is the same.