Difference between Earthing Reactor and Earthing Transformer

By 'Earthing transformer' you mean a Zigzag winding transformer, I suppose. Normally, zigzag winding transformer is used to provide earth reference for an unearthed systems such as Delta tertiary side in the subject three winding transformer.
I have seen Resistor being connected to the neutral of the zigzag transformer but not reactor.
So, Zigzag earthing transformer and Earthing resistor are used together. Zigzag transformer to provide earth reference to the unearthed system and the neutral earthing resistor to limit the magnitude of the earth fault current in the system.

R Raghunath

The Earthing Reactor (Earthing Impedance) and the Earthing transformer are complimentary.
The earthing Transformer connects to the three phase grid to provide a single phase ground reference.
The Earthing impedance limits the ground fault current.

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Ohm's law
Not just a good idea;
It's the LAW!

If the tertiary is not loaded, one corner is kept earthed to avoid power frequency transferred overvoltages. An earthing transformer is used for extensive tertiary lines. Neutral earthing through the resistor is used to limit ground fault current, and the reactor is used to limit arc flash current in case of a ground fault in tertiary circuits. Normally, both are not required for the transformers mentioned by you.