Synthetic aperture radar (SAR) has become indispensable for target interpretation owing to its all-day and all-weather observation capability. In SAR target interpretation, electromagnetic scattering information provides a physically grounded cue beyond visual texture and has been widely exploited for target interpretation. However, existing methods remain dominated by local scattering center representations. Such unordered and component-agnostic representations are highly unstable for aircraft targets. As a result, physically existing components with weak scattering responses are often missed, resulting in the incomplete reconstructed topology structure. To address this limitation, we establish Semantic Scattering Structure Understanding as a new paradigm for SAR aircraft interpretation. Semantic scattering keypoints are defined to associate local electromagnetic responses with physically meaningful aircraft components, while visibility-aware attributes are introduced to retain weakly observable yet physically existed components. The keypoints are further organized into a stable semantic scattering structure. Build upon this, we propose S3U-SAR, a physics-driven framework to localize semantic scattering keypoints and construct the complete representation constrained by multi-dimensional physical priors containing scattering heterogeneity, rigid-body topology, speckle uncertainty. A confidence-gated joint supervision strategy is further introduced to alleviate optimization conflicts. We construct KP-SAR-Aircraft-1.0, the first fine-grained benchmark for semantic scattering structure understanding. Extensive experiments demonstrate that S3U-SAR achieves the best performance compared with baselines. Cross-category and cross-dataset evaluations further verify its robustness and transferability.