Generalizing tool manipulation requires both semantic planning and precise physical control. Modern generalist robot policies, such as Vision-Language-Action (VLA) models, often lack the high-fidelity physical grounding required for contact-rich tool manipulation. Conversely, existing contact-aware policies that leverage tactile or haptic sensing are typically instance-specific and fail to generalize across diverse tool geometries. Bridging this gap requires learning unified contact representations from diverse data, yet a fundamental barrier remains: diverse real-world tactile data are prohibitive at scale, while direct zero-shot sim-to-real transfer is challenging due to the complex dynamics of nonlinear deformation of soft sensors. To address this, we propose Semantic-Contact Fields (SCFields), a unified 3D representation fusing visual semantics with dense contact estimates. We enable this via a two-stage Sim-to-Real Contact Learning Pipeline: first, we pre-train on a large simulation data set to learn general contact physics; second, we fine-tune on a small set of real data, pseudo-labeled via geometric heuristics and force optimization, to align sensor characteristics. This allows physical generalization to unseen tools. We leverage SCFields as the dense observation input for a diffusion policy to enable robust execution of contact-rich tool manipulation tasks. Experiments on scraping, crayon drawing, and peeling demonstrate robust category-level generalization, significantly outperforming vision-only and raw-tactile baselines.