Existing continuum robots with nonstretchable skeletons are monofunctional, providing only bending degrees of freedom (DOF). Additionally, their nonembedded solid structures limit application potential. In this study, inspired by origami structures, a cable‐driven continuum robot featuring dual bending‐contraction DOF is developed. Then, kinematic analysis to predict deformation at different cable contraction and joint parameters is conducted. Based on the kinematic characteristics of the robot, a continuum robot with five joint modules is fabricated to demonstrate its contraction and bending capabilities under no‐load and loaded states. This continuum robot can reach a maximum contraction of 33.87% and a bending angle of 95.71°. By increasing the number of joints in the continuum robot, grippers with different numbers of fingers can be made for grasping objects of various shapes. Additionally, based on the embedded characteristics of the robot's cable‐supported structure, a wrist rehabilitation orthosis with two joint modules is designed. This orthosis supports personalized customization, and has two rehabilitation movement modes, that is, flexion‐extension (76.45° curvature) and radial‐ulnar deviation (53.66° curvature). The performance and application experiments demonstrate the robot's structural conformality and potential for application in different interaction scenarios, and provide the practical guidance for cable‐driven continuum robotic applications.