Numerical models play a fundamental role in the development of marine hydrokinetic (MHK) turbines, as they can evaluate their performance and assess interactions with the local environment. Actuator representations that incorporate a force in the momentum equation of the flow are commonly used in numerical models to study the complex dynamics of wakes generated by the devices. However, the implications of adopting any of these approaches in simulations of turbulent wakes are not yet clear. To understand the effects produced by different approaches, we carry out simulations using a coherent-structure resolving turbulence model, for which we test three actuator representations: Actuator Disk, Blade-Element Momentum, and Actuator Lines. We reproduce an experiment with a horizontal-axis turbine and show the influence of each formulation on the mean flow and on the dynamics of the wake. In all three cases, unsteady large-scale vortices govern the flow statistics, but while the mean flow is captured reasonably well by all models, they produce structures of different scales and rotational features that control the details of wake recovery. These new insights can help define the most appropriate model for each specific flow and improve predictions at different spatial scales in future investigations.