Knowing That and Knowing How
The distinction between knowing that (propositional knowledge) and knowing how (practical or procedural knowledge) was systematized by Gilbert Ryle in The Concept of Mind (1949), though it draws on older philosophical discussion. Knowing that P is having a belief that P is true, with appropriate justification. Knowing how to V is possessing the capacity to perform V skillfully — which may not decompose into any set of propositions.
A concert pianist knows how to play Chopin. Attempting to reduce this know-how to a set of propositions the pianist 'has in mind' while playing leads immediately into Ryle's regress: if every intelligent performance requires the prior application of a rule, then applying the rule is itself a performance requiring a prior rule, and so on without end. The regress is blocked only by acknowledging that some knowledge is constituted by the capacity itself — not by a propositional description of the capacity.
This has acute implications for Artificial Intelligence: systems trained on text corpora accumulate vast propositional knowledge, but whether that propositional training transfers to genuine competence — to the kind of context-sensitive, adaptive, embodied performance that constitutes know-how — is a genuinely open question. The distinction suggests that language models trained on descriptions of swimming are not thereby acquiring know-how about swimming, however accurate those descriptions. Whether the same asymmetry applies to cognitive rather than physical domains is less clear, and it is precisely where the interesting arguments live.
See also: Gilbert Ryle, Tacit Knowledge, Procedural Memory, Artificial Intelligence.