The ability to visually track, using smooth pursuit eye movements, moving objects is critical in both perceptual and action tasks. Here, by asking participants to view a moving target or track it with their hand, we tested whether different task demands give rise to different gaze strategies. We hypothesized that during hand tracking, in comparison to eye tracking, the frequency of catch-up saccades would be lower, and the smooth pursuit gain would be greater, because it limits the loss of stable retinal and extra-retinal information due to saccades. In our study participants viewed a visual target that followed a smooth but unpredictable trajectory in a horizontal plane and were instructed to either track the target with their gaze or with a cursor controlled by a manipulandum. Although the mean distance between gaze and target was comparable in both tasks, we found, consistent with our hypothesis, an increase in smooth pursuit gain and a decrease in the frequency of catch-up saccades during hand tracking. We suggest that this difference in gaze behavior arises from different tasks demands. Whereas keeping gaze close to the target is important in both tasks, obtaining stable retinal and extra-retinal information is critical for guiding hand movement.