Differences Between Moments and Angular Displacements in Cylindrical Coordinate System in Mechanical

There are so many issues with this explanation, I don't think anything is 100% incorrect, but you haven't actually explained why the difference occurs. In all cases the nodal CS will not update because all of these analyses are all linear static structurals (correct me if I am wrong if they have large deformations active). It is not purely due to the nodal CS not updating that this difference occurs. You then apply a force using the direct method then talk about surface elements, which isn't utilised if the force is applied directly, this uses the F command. You also fail to mention that the stress contours between the cases are different, and don't explain why that would be, and you also don't mention that there are competing constraints/displacements at the edges of your model (when the load is applied as a displacement), where the peak stress is occuring.