It is widely known that the pinch-grip forces of the human hand are linearly related to the weight of the grasped object. Less is known about the relationship between grip force and grip stiffness. We set out to determine variations to these dependencies in different tasks with and without visual feedback. In two different settings, subjects were asked to (a) grasp and hold a stiffness-measuring manipulandum with a predefined grip force, differing from experiment to experiment, or (b) grasp and hold this manipulandum of which we varied the weight between trials in a more natural task. Both situations led to grip forces in comparable ranges. As the measured grip stiffness is the result of muscle and tendon properties, and since muscle/tendon stiffness increases more-or-less linearly as a function of muscle force, we found, as might be predicted, a linear relationship between grip force and grip stiffness. However, the measured stiffness ranges and the increase of stiffness with grip force varied significantly between the two tasks. Furthermore, we found a strong correlation between regression slope and mean stiffness for the force task which we ascribe to a force stiffness curve going through the origin. Based on a biomechanical model, we attributed the difference between both tasks to changes in wrist configuration, rather than to changes in cocontraction. In a new set of experiments where we prevent the wrist from moving by fixing it and resting it on a pedestal, we found subjects exhibiting similar stiffness/force characteristics in both tasks.