Highly concentrated electrolytes based on Li-salts and chelating solvents, such as glymes, are promising as electrolytes for lithium batteries. This is due to their unique properties, such as higher electrochemical stabilities, compliance with high-voltage electrodes, low volatility and flammability, and inertness toward aluminum current collector corrosion. The nature of these properties originates from the molecular-level structure created in either solvate ionic liquids (SILs) or the less common ionic aggregates by disproportionation reactions. The nature of the anion plays a crucial role, and here, we present a computational study using TFSI and TDI anions as probes, revealing increasing differences upon increased salt concentration. TFSI-based electrolytes preferably form SILs, while TDI-based electrolytes form ionic aggregates. The latter lead to an unexpected creation of "free" cationic species even at (very) high salt concentrations and thus promise of ample lithium ion transport.