The wind stress  acting on the ocean surface is usually parameterized using the turbulent drag formula
where  is the turbulent drag coefficient (usually determined empirically),  is the air density, and  is the wind velocity vector, usually taken at 10m above sea level. This parameterization is commonly referred to as resting ocean approximation. From now on we will refer to wind stress in resting ocean approximation as simply resting ocean wind stress.
On the other hand, relative wind stress  makes use of the velocity of the surface wind relative to the velocity at the ocean surface , as follows,
where  is the surface ocean velocity and thus, the terms with  represent the wind velocity relative to the surface ocean velocity. Therefore, the difference between wind stress and relative wind stress is that relative wind stress takes into account the relative motion of the wind with respect to the surface ocean current.