Starting from the physical equivalence between the quantum Rabi model and Jaynes-Cummings (JC) model under weak-coupling condition, rotating wave approximation, eigen energy, and dynamical evolutionof the two models are compared and analyzed, and the similarities and differences between the two models under the conditions of strong coupling and even ultra-strong coupling are summarized. Based on the physical principle that electromagnetically parametric amplification can enhance the atom-photon coherent coupling, the corresponding physical image of the transition from weak-coupling JC model to strong-coupling Rabi model is discussed. The numerical simulation results show that based on its difference and inherent relation of the ground states for the two models, the preparation of steady-state Schrdinger cat states can be realized with high efficiency by utilizing the proposed adiabatic ground-state transition scheme.