Earth Fault and Ground Fault is intended to mean the same thing. I think Ground Fault is North American ad Earth Fault is probably everywhere else, certainly Europe. Drives built as "worldwide" drives will usually say Earth Fault.
How is it measured? The simplest description is that the current leaving the drive off of the positive rail of the DC bus is compared to the current returning on the negative rail of the DC bus. Within very small tolerances, if there is a difference, the conclusion is drawn that some of the current that went out there to the motor didn't come back! As in leakage to ground! This difference monitoring creates the Earth Fault.
Unfortunately, there are numerous complexities that can make nuisance faulting a big headache. That's why the fault can be turned off in Group 30 Parameter 17.
I am not a drive repair person or a drive designer so the internals are not my strong suit. Having said that, externally, the drive Earth Fault detection works best when the incoming AC power is voltage balanced to ground and referenced to ground. That would be a grounded wye or star power source. Imbalance leads to false faulting due, as I am told, to capacitance between the two DC bus rails and the drive frame (which is grounded) causing imbalanced currents in the DC bus rails. Further complicating matters are EMI and RFI filter networks that are mandated by stringent European laws. These filter networks must contact the drive chassis ground and, again as I am told, try to pull the DC bus into balance with ground. If the supply is not balanced or is floating, false faulting results and, in some cases, the filter networks burn up. ABB states in their installation manuals that these networks must be disconnected from ground on floating and imbalanced supplies to avoid drive damage.