This work presents a systematic study of hybrid modeling techniques that combine physics-based white-box models with data-driven black-box components to compensate for systematic discrepancies in dynamic system models. A nonlinear three-mass oscillator with external excitation serves as a representative benchmark, enabling controlled assessment of accuracy, robustness, and generalization. Five hybrid procedures are examined: discrete correction in the state space and output space, continuous correction of the system dynamics, force-based continuous correction, and continuous correction on the output-derivative level. These approaches differ in correction layer, mathematical formulation, and required system information, allowing a structured comparison of their underlying characteristics. Comprehensive evaluations are performed across structural variants, step-size choices, transient and stationary behavior, optimized and perturbed system parameters, linearized model structures, and various uncertainty scenarios including noise, offset, and trend. Generalization properties are further assessed through interpolation and extrapolation of amplitude–frequency combinations. The results show that all hybrid methods substantially improve the predictive quality of the white-box model, with the force-based continuous procedure achieving the highest accuracy. Discrete and dynamical approaches offer stable long-term behavior with moderate input dimensionality, while output-level procedures perform well when only partial measurements are available. The study highlights the importance of the correction domain for robustness and sensitivity. Overall, these findings provide guidance for selecting appropriate hybrid modeling strategies depending on available measurements, model accessibility, and required fidelity, and connect to recent developments in discrepancy modeling and hybrid learning frameworks.