Floating wind turbines have the potential to enable global exploitation of offshore wind energy, but there is a need to further understand the complex aerodynamic phenomena they can encounter due to floater induced rotor motion. Aerodynamic models traditionally used in the wind energy sector, like the Blade Element Momentum (BEM) theory, may not be capable of capturing the dynamic phenomena that occur when the rotor moves in and out of its own wake. In the present paper, we therefore compare an industry standard BEM‐based code to a state of the art vortex solver, to investigate the phenomena in detail and further clarify the capabilities and limitations of both methods. An initial benchmark of the two codes using the IEA Wind 15 MW RWT mounted on the WindCrete spar‐buoy floater is carried out. Three different scenarios are taken into account: a bottom‐fixed, a floating case, and a floating case subject to regular waves. Growing discrepancies between the codes have been observed with the increasing complexity of the simulations. Moreover, large differences between the wake generated by a bottom fixed and a floating turbine have been observed, with the latter one experiencing a faster recovery. To further explore the floating turbines behaviors that can affect the rotor performance and wake, a systematic investigation of the mean tilt angle influence in the wake development has been carried out. Further, to account for the oscillatory motion of a floating turbine, a parametric study where the floater motion is prescribed in both pitch and surge degrees of freedom (DoF) is designed. The study covers a large variety of scenarios; a wide range of relevant frequencies and amplitudes are taken into account in under and above‐rated wind conditions. A total of more than 28 unique cases have been defined and simulated with both fidelity models. The results include the downstream evolution of the wake recovery and intensity of the turbulent disturbances induced by the rotor. The generic nature of the study allows to characterize the flow and performance effects and enables subsequent generalization to floater designs of given natural frequency and motion amplitude. It has been found that the BEM and LL predictions of the maximum loading in the blade root and tower bottom compare quite well, except for the case of large oscillation frequency in above rated conditions, where the BEM method under‐predicts the loads. Moreover, the use of a vortex solver makes it possible to look in depth into the wake characteristics, in which large differences are observed between the bottom‐fixed and the floating case in non‐turbulent inflow conditions. It has been found that the frequency and amplitude of the turbine oscillations can have a strong impact on the recovery of the wake. Moreover, we have found a link between short time intervals of large FA blade tip displacements and a faster break down of the wake. Finally it has been shown that a floating wind turbine with large and fast oscillations can transition between the differ...