Performing two skills, such as swinging a tennis racquet or axe, requires both differences in typical motor output and different feedback-driven adjustments. The motor cortex (M1) is clearly involved in specifying motor output. Less-well understood is the extent and nature of its role in performing computations underlying skill-specific feedback control. In addressing this question, a technical hurdle is that it can be difficult to discern when skill-specific aspects of neural activity reflect different motor outputs versus skill-specific feedback control. To overcome this hurdle, we employed a simple 1D force production task with two contexts that required the same typical motor output, but opposite responses to sensory feedback. Using primate Neuropixels, we recorded thousands of neurons from M1 and dorsal premotor cortex. Despite the simplicity of motor output in this task, most neurons had complex time-dependent patterns of activity that did not directly reflect force or muscle activity, and were strongly context dependent. This demonstrates something unexpected: identical motor outputs can be driven by very different internal patterns of neural activity, even in an area closely tied to motor output. Context-dependent activity presumably enables transformation of the same sensory feedback into different motor corrections. Network simulations suggest this occurs via a simple mechanism: context-dependent neural trajectories allow each context to leverage different dynamics to transform the same sensory feedback into opposing outputs. The empirical data agreed with this hypothesis: small deviations from the typical neural trajectories reflected sensory inputs, motor corrections, and the flexible link between them. These results argue that skills are produced by skill-specific (not output-specific) neural trajectories that allow for flexible input-output relationships produced by dynamics close to that trajectory. A prediction of this hypothesis is that motor cortex activity may leverage the vast volume of a high-dimensional neural space to store the repertoire of distinct motor skills.