Currently when within ArcGIS Online and using ESRI Basemaps the Measuring Tool makes area calculations using the ellipsoid-based geodesic calculation. Meanwhile if one works in that same environment with an editable hosted feature class that is a polygon, the Shape_Area field used in that polygon, will be calculated planimetrically. So essentially for the same polygon area on the map when using the Measuring Tool and then an editable hosted polygon feature class one is getting different results when one would expect to see similar if not equal values for the area in question.
Would be nice to have some consistency. Taking this further to where the end-user of the Measuring Tool and/or the hosted feature class may not be a GIS professional and you are asking for confusion and error.
Why not just use the Measuring tool? Storing the areas in a feature class allows one to preserve the numbers (enabling one to share them) and also do further analysis against them.