AC electroosmotic micropumps are suggested to be powerful tools for electrolyte dosing in various micro- and nanofluidic systems. In this paper, we compare two modeling approaches for studying the AC electroosmosis in the following micro and nanochannel systems: (i) a traveling-wave AC pump with a spatially continuous wave of electric potential applied on a planar boundary, (ii) a traveling-wave AC pump with a wave of electric potential applied on a set of discrete planar electrodes, and (iii) an AC pump with a set of non-planar electrodes. The equilibrium approach is based on the use of capacitor-resistor boundary conditions for electric potential and the slip boundary conditions for velocity at electrode surfaces. The non-equilibrium approach uses the mathematical model based on the Poisson equation and the non-slip boundary conditions. We have observed discrepancies between the predictions given by the both models and then we have identified their possible reasons. The comparison of the equilibrium and non-equilibrium results further showed three important actualities: (a) how the equilibrium model overestimates or underestimates the net velocity, (b) how the velocity maxima in the frequency characteristics can be shifted, if the equilibrium model assumptions are not satisfied, (c) the parametric region where the equilibrium model is applicable. Because the data are obtained in a dimensionless form, they can be exploited for AC electroosmotic studies. We discuss the limitations of the equilibrium and non-equilibrium models and compare selected predictions with available experimental data.