This paper studies and compares the gap selection process of multiple vehicle classes (passenger cars, delivery vans, and trucks) within their discretionary lane changing activities. Given a trajectory or a sequence of gap selection decisions, we aim to predict whether a vehicle will change or keep a lane. For this purpose, we use a large trajectory dataset, collected for the Netherlands, consisting of 3,647 trajectories of passenger car drivers, 1,080 trajectories of delivery van drivers, and 2,226 trajectories of truck drivers. We apply gated recurrent unit neural networks to separately model their gap selection processes. These three models can not only handle class imbalance but also capture long-term interdependencies. The models can predict gap selection of three vehicle classes with geometric mean accuracies of 84% or higher.To obtain insights into their gap selection processes, we apply a gradient-based technique to analyze what neural networks have learned. Our results suggest that there exist significant differences between vehicle classes in terms of the importance of historical information and features. Trucks seem to value a relatively longer period, recent 6 seconds, of driving experience to select gaps compared to passenger cars and delivery vans. In addition, the perception of road topology seems to be a significant factor for delivery vans and trucks, contrary to passenger cars which highly value their kinematic features and interactions with surrounding vehicles, to select gaps. These insights offer a novel contribution towards better understanding and modeling of the driving behavior of multiple vehicle classes.