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The difference is that in classical physics we assume a deterministic behavior, i.e., in classical physics all observables always take determined values, no matter in which state the system is "prepared" in. In quantum theory the state determines, which observables take determined values. The physical content of the quantum state is probabilistic and only probabilistic, i.e., for each observable it gives probabilities for the outcomes of measurements and nothing else. An observable's value is determined if and only if with probability 1 you measure this one value.