Classical conditioning normally requires multiple experiences, such as Pavlov's dogs salivating after they learned to associate the ringing of a bell with feeding. Memory requires only one experience, such as the time I first met my future wife.
Operant conditioning, such that an action is required to get the desired stimulus, like a dog treat when Fido sits when you say "sit", obviously requires more than classical conditioning. Still may not rise to the level of actual memory, however.
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