The default triangulated setting is recommended when the entire boundary of the stockpile is visible, and the surface is relatively flat. “Align with the lowest point” is recommended when part of the boundary is not visible, for example, the stockpile is partially surrounded by walls. So, the right volume to use in this case would be the one based on the triangulated option. The description of the base surface settings can be found here 208652926.
After looking at your results, It seems like there has been some mistake while marking the vertices that is why you are getting a massive difference in two measurements. Lowest point option uses the base surface that is parallel to the XY plane with altitude at the lowest height of all vertices. So, the error on marking the vertices can cause a massive change in volume.