Accurate pain assessment is essential for effective management; however, most studies have focused on differentiating pain from non-pain or estimating pain intensity rather than distinguishing between distinct pain types. We present a machine learning method for classifying physical and social pain using physiological signals. Seventy-three healthy adults participated in experiments involving baseline, neutral, and pain-inducing stimuli related to both types of pain. Physical pain was elicited by pressure cuff inflation, whereas social pain was induced by watching a video depicting a loved one's death. The electrocardiogram, electrodermal activity, photoplethysmogram, respiration, and finger temperature were recorded, and 12 physiological features were extracted. Three machine learning algorithms-logistic regression, support vector machine, and random forest-were employed to classify the input data into baseline versus painful states and physical versus social pain. Our findings demonstrated high accuracy in identifying social pain (0.82) and physical pain (0.90) compared to the baseline. Classification accuracy between physical and social pain was moderate (0.63) when using painful state data alone but improved to 0.77 when incorporating reactivity from neutral to painful states. This study highlights the potential of multimodal physiological signals for differentiating pain types and enhancing personalized pain management strategies.