Quantum correlation differs from classical correlation primarily through the concept of entanglement, where particles exhibit non-classical correlations. In classical optics, correlations can be analyzed using coherence theory, exemplified by laser beams. The correlation function in quantum mechanics, represented as <B(t)B(s)>, indicates the relationship between observables at different times, suggesting that if the correlation function does not vanish, the observables are dependent on each other over time. This implies that the value of an observable at one time can influence the value of another observable at a different time. Understanding these distinctions is crucial for grasping the fundamental principles of quantum mechanics.