Occasionally experimenting in arcmap with openstreetmaps basemap and in google maps i noticed something strange. I measure the distance of 2 locations in google maps (screenshot 1) and on another website which uses osm service http://www.pifpafpuf.de/cycleroute.html (screenshot 2) and the distance appears to be correct nearly the same. When i measure the same distance in arcmap 10.3 (screenshot 3) with the measure tool Line measurement (Planar) it changes a lot , exactly there is a difference of nearly 50 km. I know this maps use the same projection method WGS_1984_Web_Mercator_Auxiliary_Sphere EPSG 3857. I do not understand why does this big difference occur.
A lot of online services display in WGS84 Web Mercator, which calculates distances terribly, so they calculate distance along the ellipsoid (geodetic distance) in the background, rather than the direct planar distance. (Whether they are using the correct ellipsoid formula or not is for another question.)
ArcMap is more of a professional tool and makes no assumption, so distance calculations are done as-is; it does not check whether the projection is a good fit for the data or not.