Offshore Wind Turbines (OWTs) are subjected to complex external loadings caused by combined wind and wave sources. The application of structural damping control techniques to OWTs using Tuned Mass Dampers (TMDs) has shown to be effective in reducing the integrated system loads and accelerations. In this work, the impact of passive and semi-active (S-A) TMD?s applied to both fixed-bottom (monopile) and floating (tension leg platform) OWTs are evaluated under the Fatigue Limit State (FLS) and Ultimate Limit State (ULS). Different S-A control logics like ON/OFF state damping based on the ground hook (GH) control policy are implemented, and the frequency response of each algorithm is investigated. It is shown that the performance of each algorithm varies according to the load conditions such as FLS (normal operation) and ULS (idling state). Fully-coupled time domain simulations are conducted through the developed simulation tool for structural control integrated into the high-fidelity wind turbine design code, FASTv8. Compared to the passive TMD, it is shown that a S-A TMD results in higher load reductions, as well as, smaller strokes under both FLS and ULS conditions. In FLS analysis, the S-A TMD using Displacement Based Ground Hook (DB-GH) control is capable of reducing the fore-aft and side-to-side damage equivalent loads for the monopile substructure by approximately 12 % and 64 %, respectively. The ultimate loads at the tower base for the floating substructure (TLP) are also reduced by 9% with S-A TMD followed by Inverse Velocity Based Ground Hook control (IVB-GH). The dynamic characteristics and practical feasibility of a magnetorheological (MR) damper (for S-A control) are also evaluated.