As federated learning (FL) continues to advance, research has branched into two directions: enhancing the individual global model and developing multiple personalized models. However, few studies took both orientations into consideration in parallel. The underlying reason lies in the objective heterogeneity between global and personalized models, where the former emphasizes generalization, while the latter focuses on specialization. The dilemma of sacrificing the personalized deviation in exchange for stable global enhancement, or forsaking the global model for personalization, is particularly acute in highly heterogeneous data scenarios (as a curse). To establish the coexistence of global and personalized models in highly heterogeneous data scenarios, we propose FedAKD, a generalized federated learning framework with adaptive knowledge distillation to optimizes both global and personalized models. Specifically, based on the similarity of predictive distributions over a reference dataset, two distinct adaptive weighting strategies are employed to match the divergent focuses of global and personalized optimization, leveraging data heterogeneity to foster cooperative adaptation and establish their coexistence (as a blessing). The client-side strategy through cluster-oriented optimization to facilitate the domain adaptation in local tasks. Meanwhile, the server-side strategy adjusts the global model to accommodate varying optimization directions from diverse implicit clusters. Experiments in label and feature shift settings demonstrate that our method outperforms state-of-the-art methods in both global and personalized performance with faster convergence [e.g. the accuracy improvements on the physical activity monitoring dataset (PAMAP2) for global and personalized models exceed 26.51% and 11.00%, respectively]. Furthermore, our method is equally applicable to real-world healthcare scenarios.