In murine primary visual cortex, simple cells extract edge orientation from visual inputs, while complex cells extract motion direction. These properties are classically measured using synthetic psychophysical visual stimuli, typically drifting gratings. Natural movies contain complicated distributions of edge orientation and motion statistics, vastly differing from the edge and motion content of drifting gratings. It remains unclear the extent to which single neuron properties measured under synthetic stimuli extend to responses to natural movies. In this study, we use two-photon calcium imaging in 6 mice (both sexes) to measure the response to optimal frequency square wave gratings and water flow, each rotated into 8 directions. We find these stimuli recruit an overlapping neural population, recruited slightly stronger (signed rank test on average response across trials and directions, p = 1.7e-5, r = 0.097, n = 981), but more reliably (rank sum test on variance explained by tuning curve: p = 1.7e-8, r = 0.211, n = 225), to water than gratings. Water flow drives direction tuning in 50% more neurons than gratings (of n=2116, 18% direction tuned to G; 33% direction tuned to W). As predicted by a linear-nonlinear edge detector model and a motion energy model, edge extracting neurons have unrelated tuning across stimulus class (in water flow movies, edge orientation is not correlated with motion direction), while motion extracting neurons are tuned to similar directions across stimulus statistical context.