Deep learning has demonstrated radiograph screening performances that are comparable or superior to radiologists. However, recent studies show that deep models for thoracic disease classification usually show degraded performance when applied to external data. Such phenomena can be categorized into shortcut learning, where the deep models learn unintended decision rules that can fit the identically distributed training and test set but fail to generalize to other distributions. A natural way to alleviate this defect is explicitly indicating the lesions and focusing the model on learning the intended features. In this paper, we conduct extensive retrospective experiments to compare a popular thoracic disease classification model, CheXNet, and a thoracic lesion detection model, CheXDet. We first showed that the two models achieved similar image-level classification performance on the internal test set with no significant differences under many scenarios. Meanwhile, we found incorporating external training data even led to performance degradation for CheXNet. Then, we compared the models' internal performance on the lesion localization task and showed that CheXDet achieved significantly better performance than CheXNet even when given 80% less training data. By further visualizing the models' decision-making regions, we revealed that CheXNet learned patterns other than the target lesions, demonstrating its shortcut learning defect. Moreover, CheXDet achieved significantly better external performance than CheXNet on both the image-level classification task and the lesion localization task. Our findings suggest improving annotation granularity for training deep learning systems as a promising way to elevate future deep learning-based diagnosis systems for clinical usage.