difference between warning and a fault in Linear Technologies chip
In general a warning means something could go wrong if unchecked, and fault means something has gone wrong. A short circuit of the output would be a fault.

Take the LTM4677 internal temperature fault and warning as an example. If a temperature warning (130C) is given it means that the device is working, but EEPROM access is disabled. At 160C the fault threshold is triggered, and the output is disabled.