Earthing is a safety measure taken to prevent humans from getting electrocuted.
It means connecting non-current carrying parts of equipment to earth, this way in case of any fault in the system, the current gets leaked to earth.
Grounding:
Grounding is also a safety measure.
It protects the entire power system from malfunctioning due to heavy spikes of electric current.
In case of grounding, the current-carrying parts are directly connected to the ground. It has a return path for leakage current as a portion of the main live wire is led under the ground.