The growing popularity of electric vehicles generates a large amount of retired lithium-ion batteries (LIBs), which, if improperly managed, can cause irreversible harm to the ecosystem. In addition to materials recovery, the topic of repurposing retired LIBs is currently receiving increasing attention. This study proposes and assesses three classification criteria—capacity, resistance, and a composite of both—to enable more effective classification of retired batteries according to various consistency requirements and real-world application purposes. Instead of the battery capacity, which is often time-consuming to acquire, multiple aging features quickly obtained from the incremental capacity analysis curves, the electrochemical impedance spectroscopy curves, and the current curves during the constant-voltage charging process are employed to classify the retired batteries under different criteria. The accuracy of the classification is tested by utilizing the features extracted from these curves as the input to four supervised machine learning (ML) models, namely CatBoost, random forest, support vector machine, and deep neural networks. A detailed comparison is made across different classification criteria, aging features, and the adopted ML models. We demonstrate that the accuracy of classification depends on the selection of features for each criterion. There is an optimal aging feature that enables the classification to reach an accuracy rate of over 95%.