Federated learning (FL) has been introduced to the healthcare domain as a decentralized learning paradigm that allows multiple parties to train a model collaboratively without privacy leakage. However, most previous studies have assumed that every client holds an identical label set. In reality, medical specialists tend to annotate only diseases within their knowledge domain or interest. This implies that label sets in each client can be different and even disjoint. In this paper, we propose the framework FedLSM to solve the problem Label Set Mismatch. FedLSM adopts different training strategies on data with different uncertainty levels to efficiently utilize unlabeled or partially labeled data as well as class-wise adaptive aggregation in the classification layer to avoid inaccurate aggregation when clients have missing labels. We evaluate FedLSM on two public real-world medical image datasets, including chest x-ray (CXR) diagnosis with 112,120 CXR images and skin lesion diagnosis with 10,015 dermoscopy images, and show that it significantly outperforms other state-of-the-art FL algorithms. Code will be made available upon acceptance.