Wearable physiological signals exhibit strong nonlinear and subject-dependent behavior, challenging traditional linear models. This study provides a unified evaluation of cognitive load, stress, and physical exercise recognition using three public Empatica~E4 datasets. Across all conditions, nonlinear machine learning models consistently outperformed linear baselines, achieving 0.89--0.98 accuracy and 0.96--0.99 ROC--AUC, while linear models remained below 0.70--0.73 AUC. Although Leave-One-Subject-Out validation revealed substantial inter-individual variability, nonlinear models maintained moderate cross-person generalization. Ablation and statistical analyses confirmed the necessity of multimodal fusion, particularly EDA, temperature, and ACC, while SHAP interpretability validated these findings by uncovering physiologically meaningful feature contributions across tasks. Overall, the results demonstrate that physiological state recognition is fundamentally nonlinear and establish a unified benchmark to guide the development of more robust wearable health-monitoring systems.