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Humans have a remarkable ability to learn by watching others, whether learning to tie an elaborate knot or play the piano. However, the mechanisms that translate visual input into motor skill execution remain unclear. It has been proposed that common cognitive and neural mechanisms underpin learning motor skills by physical and observational practice. Here we provide a novel test of the common mechanism hypothesis by testing the extent to which certain individual differences predict observational as well as physical learning. Participants (N=92 per group) either physically practiced a five-element key-press sequence or watched videos of similar sequences before physically performing trained and untrained sequences in a test phase. We also measured cognitive abilities across participants that have previously been associated with rates of learning, including working memory and fluid intelligence. Our findings show that individual differences in working memory and fluid intelligence predict improvements in dissociable aspects of motor learning following physical practice, but not observational practice. Working memory predicts general learning gains from pre- to post-test that generalise to untrained sequences, whereas fluid intelligence predicts sequence-specific gains that are tied to trained sequences. However, neither working memory nor fluid intelligence predict training gains following observational learning. Therefore, these results suggest limits to the shared mechanism hypothesis of physical and observational learning. Indeed, models of observational learning need updating to reflect the extent to which such learning is based on shared as well as distinct processes compared to physical learning. We suggest that such differences could reflect the more intentional nature of learning during physical compared to observational practice, which relies to a greater extent on higher-order cognitive resources such as working memory and fluid intelligence.