The intricate role of shear viscosity and ion-pair relaxations in ionic conductivity mechanisms and the underlying changes induced by salt concentration (c) in organic liquid electrolytes remain poorly understood, despite their widespread technological importance. Using molecular dynamics simulations employing nonpolarizable force fields for c ranging between 10-3 to 101 M, we show that the low and high c regimes of the ethylene carbonate-lithium bis(trifluoromethane)sulfonimide (EC-LiTFSI) electrolytes are distinctly characterized by η ∼ τc1/2 and η ∼ τc1, where η and τc are shear viscosity and cation-anion relaxation time scales, respectively. Our extensive simulations and analyses suggest a universal relationship between the ionic conductivity and c as σ(c) ∼ cαe-c/c0 (α > 0). The proposed relationship convincingly explains the ionic conductivity over a wide range of c, where the term cα accounts for the uncorrelated motion of ions and e-c/c0 captures the salt-induced changes in shear viscosity. Our simulations suggest the vehicular mechanism to be dominant at the low c regime, which transitions into a structural diffusion mechanism at the high c regime, where structural relaxation of ion pairs is the dominant form of ion transport mechanism. Our findings shed light on some of the fundamental aspects of the ion conductivity mechanisms in liquid electrolytes, offering insights into optimizing the ion transport in EC-LiTFSI electrolytes.