As automated vehicles (AVs) increasingly share roadways with human-driven vehicles (HDVs), understanding how pedestrians respond to different vehicle types in safety-critical interactions is essential for the safe deployment of automated driving technologies. This study extracts safety-critical pedestrian-vehicle interactions from the Argoverse 2 dataset to capture real-world crash avoidance behaviors in encounters involving AVs and HDVs. To model vehicle-type-specific pedestrian crash avoidance behavior, we develop a Smooth-Mamba Deep Deterministic Policy Gradient framework, termed SMamba-DDPG, which integrates smooth action constraints with efficient temporal representation learning. To quantify pedestrian behavioral differences, the framework trains separate crash avoidance policies for pedestrian interactions with AVs and HDVs. Results show that SMamba-DDPG outperforms baseline reinforcement learning and supervised learning models in reproducing pedestrian crash avoidance behaviors. Reconstructed trajectories demonstrate strong behavioral realism, accurately reproducing crash avoidance kinematics in both AV and HDV scenarios. Reaction time analysis shows that the model captures human-like response delays and reveals that pedestrians respond more quickly to AVs than to HDVs. Counterfactual analysis further indicates that pedestrians adopt lower crossing speeds when interacting with AVs. Large-scale safety analysis of model-generated data revealed that pedestrian-AV interactions consistently yielded lower conflict rates and higher pedestrian yielding rates compared to pedestrian-HDV interactions. The findings highlight the importance of incorporating vehicle-type-specific pedestrian behavioral models for safer automated driving system design and more realistic traffic simulations in mixed-traffic environments.