In this article we show that, analyzed in a barycentric reference frame, the deviation in conductivity measured directly from impedance experiments with respect to that estimated indirectly from NMR diffusion experiments has different origins in electrolyte solutions and pure salts. In the case of electrolyte solutions, the momentum conservation law is satisfied by solvent + ions. Instead, in a molten salt or ionic liquid momentum conservation must be satisfied solely by the ions. This has significant implications. While positively correlated motion of ions of opposite charge is a well justified explanation for the reduction in impedance conductivity in the case of electrolyte solutions, it is not so in the case of ionic liquids and molten salts. This work presents a set of equations that in the case of ionic liquids and molten salts can be used to obtain from direct measurements of impedance and NMR the distinct part of the diffusion coefficient matrix in the barycentric reference frame In other words, by using experimentally measurable quantities, these equations allow us to access the motional coupling between ions for which there is no single direct experimental measurement technique. While equations of this type have been proposed before, the ones presented here can be easily derived from the momentum conservation law and linear response theory. Our results indicate that the decrease in the impedance conductivity with respect to NMR conductivity in ionic liquids and molten salts is due to anticorrelated motion of ions of same charge. This scenario is different in electrolyte solutions, where the positively correlated motion of ions of opposite charge makes a significant contribution to the decrease in the impedance conductivity. In contrast, in a system comprising a single binary salt (a room temperature ionic liquid or a molten salt), the cation-anion distinct diffusion coefficient is negative definite and opposes the contribution from the cation-cation and anion-anion distinct diffusion coefficients. This property of the cation-anion distinct diffusion coefficient in systems comprising just two ion-constituents holds true not just in the barycentric reference frame but also in any of the internal reference frames of nonequilibrium thermodynamics.