Eye-in-hand versus eye-to-hand
Where the camera lives changes the whole character of the servoing problem. In an eye-in-hand setup, the camera is mounted on the robot itself, often near the end effector, so it moves along with the arm and gets a close, detailed view of whatever the robot is approaching. This is common in precision tasks where fine detail near the target matters more than a wide view of the whole scene.
In an eye-to-hand setup, the camera is fixed in the environment, watching both the robot and the target from a stationary vantage point. This trades away close-up detail for a stable, wide field of view that never loses sight of the workspace as the robot moves through it, which matters for tasks where the robot's own body might otherwise block a wrist-mounted camera's view of the target.