Basically there are just two type earth fault and restricted earth fault.
An earth fault is a leakage of current between any conductor that normally carries current, that is the phase and neutral conductors, and the general mass of earth and anything connected to it anywhere downstream of the point within the system that the earth fault protection device is situated. The protective device for this type of fault is often referred to as an unrestricted earth fault device.
A restricted earth fault is as above but it is within a zone that is created by the protection device any earth fault outside the zone will not be detected.
The difference between earth fault and sensitive earth fault is the settings availability of the protective device.