AbstractSurface drifter observations from the LAgrangian Submesoscale ExpeRiment (LASER) campaign in the Gulf of Mexico are paired with Eulerian (ship‐borne X‐band radar) data to demonstrate that velocity structure functions from drifters differ systematically from Eulerian structure functions over scales from 0.4 to 7 km. These differences result from drifters oversampling surface convergences and regions of intense vorticity. The first‐, second‐, and third‐order structure functions are calculated using quasi‐Lagrangian (drifter) and Eulerian data from approximately the same location and time. Differences between quasi‐Lagrangian and Eulerian structure functions are attributed to two forms of bias. The first bias results from the mean divergence or vorticity of the background flow creating nonzero first‐order structure functions. This background bias affects both quasi‐Lagrangian and Eulerian data when insufficiently time‐averaged. It severely biases the drifter third‐order structure functions but is smaller in Eulerian structure functions at both second and third order. This bias can be corrected for using lower‐order structure functions. The second form of bias results from drifters accumulating in regions with flow statistics that differ from undersampled regions. This accumulation bias is diagnosed by identifying the dependence of the Eulerian structure functions on divergence and vorticity as well as scale. Together, both biases suggest that caution is needed when interpreting second‐order drifter statistics and that linking raw third‐order drifter statistics to energy fluxes is often erroneous in ocean data: Even with background correction and sufficient time‐averaging, drifters overestimate the Eulerian estimate of the third‐order structure function by up to a factor of 5 when signs are consistent.