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In federated learning (FL), accommodating clients with diverse resource constraints remains a significant challenge. A widely adopted approach is to use a shared full-size model, from which each client extracts a submodel aligned with its computational budget. However, regardless of the specific scoring strategy, these methods rely on the same global backbone, limiting both structural diversity and representational adaptation across clients. This paper presents FRAMP, a unified framework for personalized and resource-adaptive federated learning. Instead of relying on a fixed global model, FRAMP generates client-specific models from compact client descriptors, enabling fine-grained adaptation to both data characteristics and computational budgets. Each client trains a tailored lightweight submodel and aligns its learned representation with others to maintain global semantic consistency. Extensive experiments on vision and graph benchmarks demonstrate that FRAMP enhances generalization and adaptivity across a wide range of client settings.