The solar wind gets thermalized and compressed when crossing a planetary bow shock, forming the magnetosheath. The angle between the upstream magnetic field and the shock normal vector separates the quasi-parallel from the quasi-perpendicular magnetosheath, significantly influencing the physical conditions in these regions. A reliable classification between both magnetosheath regions is of utmost importance since different phenomena and physical processes take place on each. The complexity of this classification is increased due to the origin and variability of the solar wind. Using measurements from the Time History of Events and Macroscale Interactions during Substorms mission and OMNI data between 2008 and 2023, we demonstrate the importance of magnetosheath classification across various solar wind plasma origins. We focus on investigating the ion energy fluxes in the high-energy range for each solar wind type, which typically serves as an indicator for foreshock activity and thus separating the quasi-parallel from quasi-perpendicular magnetosheath. Dividing the data set into different regimes reveals that fast solar wind plasma originating from coronal holes causes exceptionally high-energy ion fluxes even in the quasi-perpendicular environment. This stands in stark contrast to all other solar wind types, highlighting that magnetosheath classification is inherently biased if not all types of solar wind are considered in the classification. Combining knowledge of solar wind origins and structures with shock and magnetosheath research thus contributes to an improved magnetosheath characterization. This is particularly valuable in big-data machine-learning applications within heliophysics, which requires clean and verified data sets for optimal performance.