In the decades, the use of scatterometer data allowed to demonstrate the global ubiquity of the ocean mesoscale thermal feedback (TFB) and current feedback (CFB) effects on surface winds and stress. Understanding these air-sea interactions is of uttermost importance as the induced atmospheric anomalies partly control the ocean circulation and thus can influence the Earth climate. Whether the TFB and CFB effects can be disentangled, and whether satellite scatterometers can properly reveal them, remain rather unclear. Here, using satellite observations and ocean-atmosphere coupled mesoscale simulations over 45 degrees S to 45 degrees N, we show that the CFB effect can be properly characterized and unraveled from that due to the TFB. We demonstrate that the TFB can be unambiguously characterized by its effect on the stress (and wind) divergence and magnitude. However, its effect on the wind and stress curl is contaminated by the CFB and thus cannot be estimated from scatterometer data. Finally, because scatterometers provide equivalent neutral stability winds relative to the oceanic currents, they cannot characterize adequately the CFB wind response and overestimate the TFB wind response by approximate to 25%. Surface stress appears to be the more appropriate variable to consider from scatterometer data.