To gain insight into the differences between onshore and offshore atmospheric turbulence, pressure fluctuations were measured for offshore wind under different environmental conditions. A durable piezo-electric sensor was used to sample turbulent pressure data at 50 kHz. Offshore measurements were performed at 100 m height on Germany's FINO3 offshore platform in the German Bight together with additional meteorological data provided by Deutscher Wetterdienst (DWD). The statistical evaluation revealed that the stability state in the atmospheric boundary has a large impact on turbulent fluctuations. Therefore, we used higher statistical properties (described by so-called shape factors) to the stability state. Data was classified to be either within the unstable, neutral or stable stratification. We found that in case of stable stratification, the shape factor is mostly close to zero, indicating that a thermally stable environment produces closer-to Gaussian distributions. Non-Gaussian distributions were found in unstable and neutral boundary layer states and an occurrence probability was estimated. Possible impact on laminar-turbulent transition on the blade is discussed with application of so-called laminar airfoils on wind turbine blades. Use of a cut-off frequency to separate load and aerodynamic turbulence is proposed.