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This paper shows that two apparently independent models of hysteresis-the Jiles-Atherton model, developed by Jiles and Atherton, and the energetic model, developed by Hauser-are mathematically equivalent. These two hysteresis models are examined with respect to their capability to describe the dependence of the magnetization on magnetic field and mechanical stress. Comparisons have been made between the predictions of the two models and measured hysteresis curves. Through a mathematical analysis of the structure of the models, conditions have been found under which both models predict the same magnetization curves. This "common ground" agreement between the models has allowed us to establish correspondence between the descriptors of the models so that a mathematical transformation between the model parameters becomes possible. The result allows improved interpretation of the physical mechanisms that contribute to ferromagnetic hysteresis at different stages in the magnetization curve in terms of the reversible and irreversible physical processes such as domain wall motion and domain rotation which form the basis of these models. Furthermore, consideration of the internal demagnetizing factor has also allowed it to be included in the models.