The biophysical characteristics of cells determine the shape of individual cells and their packing within tissues. Cells can form regular or irregular epithelial structures, round up and form clusters,or deform and attach to substrates. The acquired shape of cells and tissues is a consequence of internal cytoskeletal processes, such as actin polymerisation and cortical myosin contraction, of adhesion molecules within the cell membrane that interact with substrates and neighbouring cells, and of processes that regulate cell volume. Although these cellular processes seem relatively simple, when combined they unleash a rich variety of cellular behaviour that is not readily understandable outside a theoretical framework. We here present through mathematical and computational analysis how the Cellular Potts Model (CPM) can be considered to form an integral part of the larger set of Cell Surface Mechanics models that describe cell surface mechanics using energy-based approaches. We show how forces and tensions can be derived and cell behaviour and tissue packing predicted, allowing for an intuitive, biologically relevant mapping between the modelling parameters and experiments. The biological insights and qualitative cellular behaviours closely agree with the analytical study, not only for the CPM, but even across different model formalisms. This illustrates the generality of energy-based approaches for cell surface mechanics and highlights how meaningful and quantitative comparisons between models can be established. Moreover, the mathematical analysis yields direct links between known biophysical properties and specific parameter settings within the CPM.