Partially supervised segmentation is a label-saving method based on datasets with fractional classes labeled and intersectant. Its practical application in real-world medical scenarios is, however, hindered by privacy concerns and data heterogeneity. To address these issues without compromising privacy, federated partially supervised segmentation (FPSS) is formulated in this work. The primary challenges for FPSS are class heterogeneity and client drift. We propose a unified federated partially labeled segmentation (UFPS) framework to segment pixels within all classes for partially annotated datasets by training a comprehensive global model that avoids class collision. Our framework includes unified label learning (ULL) and sparse unified sharpness aware minimization (sUSAM) for class and feature space unification, respectively. Through empirical studies, we find that traditional methods in partially supervised segmentation and federated learning often struggle with class collision when combined. Our extensive experiments on real medical datasets demonstrate better deconflicting and generalization capabilities of UFPS.