Federated learning (FL) is a privacy-preserving collaboratively machine learning paradigm. Traditional FL requires all data owners (a.k.a. FL clients) to train the same local model. This design is not well-suited for scenarios involving data and/or system heterogeneity. Model-Heterogeneous Personalized FL (MHPFL) has emerged to address this challenge. Existing MHPFL approaches often rely on having a public dataset with the same nature of the learning task, or incur high computation and communication costs. To address these limitations, we propose the Federated Semantic Similarity Aggregation (FedSSA) approach, which splits each client's model into a heterogeneous (structure-different) feature extractor and a homogeneous (structure-same) classification header. It performs local-to-global knowledge transfer via semantic similarity-based header parameter aggregation. In addition, global-to-local knowledge transfer is achieved via an adaptive parameter stabilization strategy which fuses the seen-class parameters of historical local headers with that of the latest global header for each client. In this way, FedSSA does not rely on public datasets, while only requiring partial header parameter transmission (thereby saving costs). Theoretical analysis proves the convergence of FedSSA. Extensive experiments demonstrate that FedSSA achieves up to higher accuracy, times higher communication efficiency, and higher computational efficiency compared to 7 state-of-the-art MHPFL baselines.