This paper addresses the problem of detecting and discriminating threats in cyber-physical systems, where the threats may be physical faults and cyber-attacks. We propose a sensor switching watermark scheme, composed of a watermark generator and a remover, both switching between a set of two larger (outer) and two smaller (inner) values. We show that threat detection and discrimination are achieved by properly setting these values and the switching times. In particular, the proposed methodology can handle a class of physical faults and a broad range of man-in-the-middle cyber attacks such as replay attacks and integrity attacks. A key feature of our methodology is the unpredictable switching time instants that entail a combination of random elements and private time seeds. In addition, we provide suitable design requirements for the time seeds and demonstrate how these are satisfied by a chaotic Lorenz system. Finally, we illustrate the effectiveness of the proposed methodology by numerical simulations. This version of the manuscript has been accepted for publication in IEEE Transactions on Automatic Control after peer review (Author Accepted Manuscript). It is not the final published version (Version of Record) and does not reflect any post-acceptanceimprovements. The Version of Record is available online at https://ieeexplore.ieee.org/document/11144517.