Fast and efficient collision detection is essential for motion generation in robotics. In this paper, we propose an efficient collision detection framework based on the Signed Distance Field (SDF) of robots, seamlessly integrated with a self-collision detection module. Firstly, we decompose the robot's SDF using forward kinematics and leverage multiple extremely lightweight networks in parallel to efficiently approximate the SDF. Moreover, we introduce support vector machines to integrate the self-collision detection module into the framework, which we refer to as the SDF-SC framework. Using statistical features, our approach unifies the representation of collision distance for both SDF and self-collision detection. During this process, we maintain and utilize the differentiable properties of the framework to optimize collision-free robot trajectories. Finally, we develop a reactive motion controller based on our framework, enabling real-time avoidance of multiple dynamic obstacles. While maintaining high accuracy, our framework achieves inference speeds up to five times faster than previous methods. Experimental results on the Franka robotic arm demonstrate the effectiveness of our approach. Project page: https://sites.google.com/view/icra2025-sdfsc.