Accurate 3D medical segmentation is limited by anatomical variability and high computational costs. While knowledge distillation (KD) offers a route for model compression, conventional methods often fail to preserve complex structures and are overwhelmed by background noise. We propose Displacement-Preserving Relational Distillation (DPRD), which distills latent anatomical trajectories via vector based alignment to preserve the orientation and relative scale of the teacher's manifold, and prevents signal dilution by anchoring distillation in task-relevant structures. Integrated into nnU-Net, DPRD outperforms established baselines on ISLES 2022 and AMOS 2022 benchmarks. Notably, on the AMOS dataset, DPRD achieves a Dice score of 85.46%, edging out the high-capacity MedNeXt teacher while significantly reducing boundary errors. Despite utilizing only ~5% of the teacher's parameters and ~3% of its FLOPs, our approach maintains high structural consistency. This provides a robust, efficient solution for deploying high performance segmenters in resource-constrained clinical environments. Code: https://github.com/ClinicaAlpha/DPRD-3D-MedSeg