Cross-tokenizer knowledge distillation, where the teacher and student employ different tokenizers, is becoming increasingly prevalent, yet it poses underexplored challenges: existing methods fail to capture the rich knowledge encoded in teacher logits, as evidenced by the neglect of semantic information, inaccurate and biased logit alignment, and discarding distributional structure—ultimately leading to unfavorable distillation. To address these issues, we propose SeDi, a semantics and distribution-aware knowledge transfer framework tailored for cross-tokenizer distillation. To preserve factual knowledge, SeDi employs bipartite graph-based alignment at the tokenization level and a sliding window re-encoding strategy at the vocabulary level, enabling unbiased transfer of the teacher’s next-token predictions into the student’s vocabulary space. To further retain distributional information, we align the student’s entropy with that of the teacher by incorporating the student’s own logits during training, which helps to mitigate the exposure bias problem. Experiments on ten datasets across three task domains and five different teacher-student model pairs with varying vocabulary sizes demonstrate that SeDi delivers substantial improvements, with gains of up to 19.8%.