A "Fault" means the tachograph equipment itself has a problem — the vehicle unit, printer, display, or downloading function malfunctioning, the motion sensor failing, or an issue with the driver card. The tachograph records these automatically, the same way it records Events.
The difference is what's being flagged:
An Event points to something about how the card or vehicle was used, like a card inserted while driving.
A Fault points to the equipment not working correctly. Infringements are different again: they aren't recorded by the tachograph at all, but calculated afterward from a driver's activity data, to check it against EU driving and rest time rules.