In the design of prosthetic hand fingers, achieving human-like movement while meeting anthropomorphic demands such as appearance, size, and lightweight is quite challenging. Human finger movement involves two distinct motion characters during natural reach-and-grasp tasks: consistency in the reaching stage and adaptability in the grasping stage. The former one enhances grasp stability and reduces control complexity; the latter one promotes the adaptability of finger to various objects. However, conventional tendon-driven prosthetic finger designs typically incorporate bulky actuation modules or complex tendon routes to reconcile the consistency and adaptability. In contrast, we propose a novel friction clutch consisting of a single tendon and slider, which is simple and compact enough to be configurated within the metacarpal bone. Through tactfully exploiting the friction force to balance the gravity effect on each phalanx during finger motion, this design effectively combines both consistency and adaptability. As a result, the prosthetic finger can maintain consistent motion unaffected by any spatial posture during reaching, execute adaptive motion during grasping, and automatically switch between them, resulting in human-like reach-and-grasp movements. Additionally, the proposed finger achieves a highly anthropomorphic design, weighing only 18.9 g and possessing the same size as an adult's middle finger. Finally, a series of experiments validate the theoretical effectiveness and motion performance of the proposed design. Remarkably, the mechanical principle of the proposed friction clutch is beneficial to achieve highly anthropomorphic design, providing not only a new strategy to prosthetic hand design but also great potential in hand rehabilitation.