This paper addresses the problem of Fault Detection and Isolation (FDI) of switching systems where faulty behaviours are represented as faulty modes. The objectives of the on-line FDI are to identify accurately the current mode and to estimate precisely the switching time. A data-based method is considered here to generate residuals that will be used for FDI. The discernibility condition between modes is established. It is claimed in the literature that discernibility conditions are necessary for switching detection. However, it is shown in this paper that the switching may be detected with the proposed residuals even if the modes are not discernible. Detectability conditions between modes are established and are shown to be different from discernibility ones. A simulation example is provided to illustrate this important result.