Earthing means connecting the dead part, it means the part which does not carries current under normal condition to the earth. For example electrical equipment’s frames, enclosures, supports etc.
While Grounding means connecting the live part (it means the part which carries current under normal condition) to the earth. For example neutral of power transformer.
The purpose of Earthing is to minimize risk of receiving an electric shock if touching metal parts when a fault is present.
While the purpose of Grounding is the protections of power system equipment and to provide an effective return path from the machine to the power source. For example grounding of neutral point of a star connected transformer.
Ground is a source for unwanted currents and also as a return path for main current some times. While Earthing is done not for return path but only for protection of delicate equipment.