Knowledge of the turbulence in the wakes of wind turbines is important to improve the operation and lifetime of downstream turbines exposed to these wakes. As the investigation of a rotating turbine can be challenging, both experimentally and numerically, static actuator discs can substitute rotating turbines. To investigate the similarity of the turbulence in the wakes and how turbulent inflow alters the result, an experimental wind tunnel study is presented that compares hot-wire measurements in the central wakes of an actuator disc and a model wind turbine (diameter-based Reynolds number Re ≈ 300000). Two turbulent inflows are investigated, an intermittent, i.e. gusty, atmospheric-like inflow generated by an active grid, and a non-intermittent inflow generated by a regular grid. The data is investigated using one-point and higher-order two-point statistics. We find that the wakes of both models have similar properties for all investigated quantities within the far wake. The turbulence in the central wake is independent of the inflow conditions, and both models filter larger scale intermittency in the far wake with regard to the inflow. Also, we find that the turbine generates its own kind of turbulence that dominates the ambient turbulence and has strong features of homogeneous, isotropic turbulence.