The growing prospect for large farms of floating offshore wind turbines requires a better understanding of wake effects for floating turbines, particularly the differences when compared to fixed-bottom turbine wakes. The increased range of motion of floating platforms can influence wake characteristics, affecting downstream turbines. In this work, large eddy simulations with an actuator line model are used to study downstream wake characteristics of the NREL 5-MW reference turbine mounted on the OC3-UMaine spar platform for several different metocean conditions. The simulations are carried out in the Simulator fOr Wind Farm Applications coupled with OpenFAST for the platform and turbine motion. The downstream wake characteristics of the floating platform are compared to equivalent fixed-bottom cases for different wind speeds, wave heights, wind-wave alignments, and turbine yaw angles. Overall, the differences in wake shape between floating and fixed platforms are associated with mean platform displacements, while differences in turbulence are associated with time-varying platform motion. However, these observed wake differences between fixed and floating platforms are small, especially for higher wind speeds and lower wave heights.