While advanced foundation models like ModernBERT significantly outperform older architectures in dense retrieval, they surprisingly lag behind the aging BERT-base baseline in learned sparse retrieval (LSR). We identify the root cause as the Vocabulary Gap : modern tokenizers utilize raw, case-sensitive vocabularies designed for lossless reconstruction, which map single semantic units to redundant surface forms, wasting model capacity on morphological noise and hindering lexical matching. We formalize this intuition through a theoretical framework, demonstrating that appropriate vocabulary coarse-graining can tighten the generalization bounds by reducing complexity of the hypothesis class, provided that semantic integrity is preserved. To resolve this, we propose Vocabulary Transfer (VT), a model-agnostic framework that migrates advanced encoders to sparse-friendly, normalized vocabularies with minimal computational cost. VT utilizes a novel Semantic Initialization via spatial topology to preserve geometric structure and an Activation Potential Calibration (APC) mechanism to align pre-trained manifolds with sparsity constraints, preventing the dead neuron and dense collapse observed in standard fine-tuning. Empirically, VT is universally effective: it enables ModernBERT to achieve state-of-the-art performance on the BEIR benchmark (52.4 nDCG, a +4.7 improvement), resuscitates failing models like RoBERTa-large, and generalizes seamlessly to inference-free architectures and specialized domains. These results confirm that the performance lag is not an architectural deficiency but a solvable vocabulary mismatch. We've released our code and models. https://anonymous.4open.science/r/vocab-transfer/. All details included.