The article explores the complexity of dynamics in the classical and semi-classical Duffing oscillator using ordinal pattern analysis. Different chaotic regimes within the system are uncovered, revealing unique patterns not seen with traditional statistical methods. A correlation between the Lyapunov exponent and permutation entropy is identified, indicating transitions in the system's dynamics. This research sheds light on the intricate behaviors of the Duffing oscillator, which has implications for experiments in the semi-classical realm.