Accurate 3D medical image segmentation is vital for diagnosis and treatment planning, but state-of-the-art models are often too large for clinics with limited computing resources. Lightweight architectures typically suffer significant performance loss. To address these deployment and speed constraints, we propose Region- and Context-aware Knowledge Distillation (ReCo-KD), a training-only framework that transfers both fine-grained anatomical detail and long-range contextual information from a high-capacity teacher to a compact student network. The framework integrates Multi-Scale Structure-Aware Region Distillation (MS-SARD), which applies class-aware masks and scale-normalized weighting to emphasize small but clinically important regions, and Multi-Scale Context Alignment (MS-CA), which aligns teacher-student affinity patterns across feature levels. Implemented on nnU-Net in a backbone-agnostic manner, ReCo-KD requires no custom student design and is easily adapted to other architectures. Experiments on multiple public 3D medical segmentation datasets and a challenging aggregated dataset show that the distilled lightweight model attains accuracy close to the teacher while markedly reducing parameters and inference latency, underscoring its practicality for clinical deployment.