Primate motor cortex projects to spinal interneurons and motor neurons, suggesting that motor cortex activity may be dominated by muscle-like commands. Extensive observations during reaching lend support to this view, but evidence remains ambiguous and much-debated. To provide a different perspective, we employed a novel behavioral paradigm that affords extensive comparison between time-evolving neural and muscle activity. We found that single motor cortex neurons displayed many muscle-like properties, but the structure of population activity was not muscle-like. Unlike muscle activity, neural activity was structured to avoid ‘tangling’: moments where similar activity patterns led to dissimilar future patterns. Avoidance of tangling was present across tasks and species. Network models revealed a potential reason for this consistent feature: low tangling confers noise robustness. Finally, we were able to predict motor cortex activity from muscle activity alone, by leveraging the hypothesis that muscle-like commands are embedded in additional structure that yields low tangling.