They will be different if you have specified a member offset. The moments reported in such a case - for the member with the offset - is not at the joint but at the face of the member, which is at the offset distance from the joint.
It can also be different if a plate or solid element is connected to that joint in addition to the column and beam. The unbalanced moment is the moment in the element at that location.
If you are referring to the moment used in concrete design, check whether it is reported at the joint, or at some distance away from the joint.
Regarding your question : The moment at the end of column is not the same as that at the start of the column of upper storey. Can this be manually adjusted?
If there are beams or slabs or shear walls framing into that column, the column below is not guaranteed to have the same moment as the column above at that joint. If you want them to be the same, you need to release the moments in all the entities framing into that joint except the columns.