Understanding the mechanisms of charge transport in batteries is important for the rational design of new electrolyte formulations. Persistent questions about ion transport mechanisms in battery electrolytes are often framed in terms of vehicular diffusion by persistent ion-solvent complexes versus structural diffusion through the breaking and reformation of ion-solvent contacts, i.e., solvent exchange events. Ultrafast two-dimensional (2D) IR spectroscopy can probe exchange processes directly via the evolution of the cross-peaks on picosecond time scales. However, vibrational energy transfer in the absence of solvent exchange gives rise to the same spectral signatures, hiding the desired processes. We employ 2D IR on solvent resonances of a mixture of acetonitrile isotopologues to differentiate chemical exchange and energy-transfer dynamics in a comprehensive series of Li+, Mg2+, Zn2+, Ca2+, and Ba2+ bis(trifluoromethylsulfonyl)imide electrolytes from the dilute to the superconcentrated regime. No exchange phenomena occur within at least 100 ps, regardless of the ion identity, salt concentration, and presence of water. All of the observed spectral dynamics originate from the intermolecular energy transfer. These results place the lower experimental boundary on the ion-solvent residence times to several hundred picoseconds, much slower than previously suggested. With the help of MD simulations and conductivity measurements on the Li+ and Zn2+ systems, we discuss these results as a continuum of vehicular and structural modalities that vary with concentration and emphasize the importance of collective electrolyte motions to ion transport. These results hold broadly applicable to many battery-relevant ions and solvents.