Improving the kinetics of electrochemical ion intercalation processes is of interest for realizing high-power electrochemical energy storage. This includes classical battery-like intercalation and pseudocapacitive intercalation processes with a capacitor-like electrochemical signature. Electrochemical methods are needed to probe the kinetics of such complex multistep processes in detail. Here, we present the use of the distribution of relaxation times (DRT) analysis of electrochemical impedance data to identify the kinetic limits of intercalation reactions. We study the lithium intercalation reaction in TiS2 from organic and aqueous electrolytes as a model system. The material can exhibit both battery-like and pseudocapacitive intercalation regimes depending on the potential range, variable diffusion lengths by adjusting its particle size, and a tunable degree of solvent cointercalation by choosing the electrolyte solvent. Using DRT, we can distinguish between the kinetic limitations imposed by solid-state ion diffusion, interfacial ion adsorption and transport, and ion desolvation processes. Thus, DRT analysis can complement existing methods, such as voltammetry or 3D-Bode analysis, to better understand the kinetics of intercalation reactions.