Turbulence is ubiquitous within space plasmas, where it is associated with numerous nonlinear interactions. Magnetospheric Multiscale (MMS) provides the unique opportunity to decompose the electric field (E) dynamics into contributions from different linear and nonlinear processes via direct measurements of the terms in generalized Ohm's law. Using high-resolution multipoint measurements, we compute the magnetohydrodynamic ( E MHD ), Hall ( E Hall ), electron pressure ( E P e ), and electron inertia ( E inertia ) terms for 60 turbulent magnetosheath intervals, to uncover the varying contributions to the dynamics as a function of scale for different plasma conditions. We identify key spectral characteristics of the Ohm's law terms: the Hall scale, k Hall , where E Hall becomes dominant over E MHD ; the relative amplitude of E P e to E Hall , which is constant in the sub-ion range; and the relative scaling of the nonlinear and linear components of E MHD and of E Hall , which are independent of scale. We find expressions for the characteristics as a function of plasma conditions. The underlying relationship between turbulent fluctuation amplitudes and ambient plasma conditions is discussed. Depending on the interval, we observe that E MHD and E Hall can be dominated by either nonlinear or linear dynamics. We find that E P e is dominated by its linear contributions, with a tendency for electron temperature fluctuations to dominate at small scales. The findings are not consistent with existing linear kinetic Alfvén wave theory for isothermal fluctuations. Our work shows how contributions to turbulent dynamics change in different plasma conditions, which may provide insight into other turbulent plasma environments.