nduced seismicity as generated by the injection of fluids in a homogeneous, permeable medium with faults with variable proximity to rupture conditions is simulated using the rate- and state-dependent frictional fault theory (RST) of Dieterich (J Geophys Res 99(B2):2601-2618, 1994) and the critical pressure theory (CPT) developed by Shapiro (Fluid-induced seismicity, Cambridge University Press, Cambridge, 2015). In CPT, the induced local seismicity density is proportional to the pressure rate, limited by the Kaiser Effect, and apparently un-related to the tectonic background seismicity. There is no time delay between a change in pressure rate and seismicity density. As a more complex theory, RST includes a time delay between a pressure change and induced seismicity and it is proportional to the natural tectonic background seismicity. Comparing both modelling approaches at a fixed location, this delay can be significant, dependent on a ‘free’ parameter that represents the lower threshold for pressure below which seismicity is not triggered. This parameter can be tuned so that the results of CPT and RST become similar. Approximations of the RST allow a new interpretation of the parameter ‘tectonic potential’ that controls the level of induced seismicity in CPT.