Sources: Byzantine Faults on Wikipedia and Paper on the Byzantine Generals Problem
A Byzantine fault is any fault presenting different symptoms to different observers.
A Byzantine failure is the loss of a system service due to a Byzantine fault in systems that require consensus between nodes.
Byzantine fault tolerance (BFT) is the property of a system that is able to resist the class of failures derived from the Byzantine Generals’ Problem. This means that a BFT system is able to continue operating even if some of the nodes fail or act maliciously.
See also: Byzantine Broadcast, PBFT