Hi!
As a reply on your first question: I wonder if this has to do with the fact that the contribution to the shift from the two distributions are scalars. The size of m_1 is a scalar and the mass contribution of m_2 at the origin as well.
This is then similar to the case of the monopole moment and the monopole field both being scalar in the monopole term. So perhaps this is the standard to call the resulting energy(shift) a monopole shift?