Bond additive indices are a special class of topological indices (TI) that are determined by the sum of the edge contributions of graphs. The Szeged index, PI index, Mostar index, and their edge versions are among the most extensively studied bond additive indices. In this paper, we investigate the difference between bond additive indices and their respective edge versions, denoted by \( \Delta TI \). Specifically, we study this problem for the Szeged index, PI index, and Mostar index. We obtain upper and lower bounds for \( \Delta TI \) for different classes of graphs such as trees, unicyclic graphs, and bicyclic graphs, and identify the graphs that attain these bounds. Furthermore, we characterize the graphs that satisfy the property \( \Delta TI = 0 \) within these graph classes.