This paper is concerned with the issue of the diagnostics of process faults and the detection of cyber-attacks in industrial control systems. This problem is of significant importance to energy production and distribution, which, being part of critical infrastructure, is usually equipped with process diagnostics and, at the same time, is often subject to cyber-attacks. A commonly used approach would be to separate the two types of anomalies. The detection of process faults would be handled by a control team, often with a help of dedicated diagnostic tools, whereas the detection of cyber-attacks would be handled by an information technology team. In this article, it is postulated here that the two can be usefully merged together into one, comprehensive, anomaly detection system. For this purpose, firstly, the main types of cyber-attacks and the main methods of detecting cyber-attacks are being reviewed. Subsequently, in the analogy to “process fault”—a term well established in process diagnostics—the term “cyber-fault” is introduced. Within this context a cyber-attack is considered as a vector containing a number of cyber-faults. Next, it is explained how methods used in process diagnostics for fault detection and isolation can be applied to the detection of cyber-attacks and, in some cases, also to isolation of the components of such attacks, i.e., cyber-faults. A laboratory stand and a simulator have been developed to test the proposed approach. Some test results are presented, demonstrating that, similarly to equipment/process faults, residua can be established and cyber-faults can be identified based on the mismatch between the real data from the system and the outputs of the simulation model.