Models of energy storage systems used for optimal energy management commonly feature unsophisticated loss expressions (lossless or constant efficiency). Preserving the tractability (i.e. convexity) of the optimization motivates this simpleness, at the expense of physical realism. Relaxing the storage loss expression from an equality constraint to an inequality allows using more complex and physically realistic models while preserving convexity. Although this relaxation has been used quite casually for a decade in varied energy management applications (power systems dispatch, electric vehicles), only few articles studied this technique for itself. To increase the awareness of loss relaxation, along with its limitations, we depict a unified view of relaxed storage loss models. Also, we propose the "convex monomial loss model", one continuously parametrized family of nonlinear convex expressions which contains all classical loss models and unlocks new possibilities for loss dependency in storage power and energy level. This is one step to reunite piecewise linear and nonlinear models which are generally studied separately. Finally, we compare the effect of these varied loss models on the optimal charge/discharge profile of a storage in an elementary energy management application.