Federated learning (FL) enables privacy-preserving collaborative model training without direct data sharing. Model-heterogeneous FL (MHFL) extends this paradigm by allowing clients to train personalized models with heterogeneous architectures tailored to their computational resources and application-specific needs. However, existing MHFL methods predominantly rely on centralized aggregation, which introduces scalability and efficiency bottlenecks, or impose restrictions requiring partially identical model architectures across clients. While peer-to-peer (P2P) FL removes server dependence, it suffers from model drift and knowledge dilution, limiting its effectiveness in heterogeneous settings. To address these challenges, we propose FedSKD, a novel MHFL framework that facilitates direct knowledge exchange through round-robin model circulation, eliminating the need for centralized aggregation while allowing fully heterogeneous model architectures across clients. FedSKD's key innovation lies in multi-dimensional similarity knowledge distillation, which enables bidirectional cross-client knowledge transfer at batch, pixel/voxel, and region levels for heterogeneous models in FL. This approach mitigates catastrophic forgetting and model drift through progressive reinforcement and distribution alignment while preserving model heterogeneity. Extensive evaluations on fMRI-based autism spectrum disorder diagnosis and skin lesion classification demonstrate that FedSKD outperforms state-of-the-art heterogeneous and homogeneous FL baselines, achieving superior personalization (client-specific accuracy) and generalization (cross-institutional adaptability). These findings underscore FedSKD's potential as a scalable and robust solution for real-world medical federated learning applications.

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