How do I know that the esr meter measures the internal resistance of the capacitor ?

[eletmoraes]

How do I know that the meter is measuring the internal resistance of the capacitor and not the reactance?

How can I identify when it is of a kind and when the other?

 

[D.A.(Tony)Stewart]

When the current is in phase with voltage, such as a high frequency square wave from a very low impedance source of current , then it is ESR.

RLC meter use a constant current source sine wave (others with pulses) and from the voltage of the sine wave determine that phase shift and amplitude. Then compute R & X