What is the relationship between social policy and public policy?

Public policy is a large umbrella that includes fiscal policy, monetary policy, international policy, and domestic policy, just to name a few areas in which government may act.  Social policy is one such area.  It is policy that is meant to address social problems, which sounds as though we could keep it in a neat little box.  It touches on so many areas of governance, though, that it may sometimes seem as though public policy is social policy.  Just to name a few areas in which this is true, education and housing are part of public policy generally, but they are also part of social policy.   Without good public education and housing security, there are many societal problems, poverty, homelessness, drugs, unemployment, and crime.  Public health is part of social policy and vice versa. Providing birth control for people is a public health issue, but it is also a solution to many social problems. Even national defense can provoke a need for social policy, to address the social problems of families of soldiers or to address the social problems when soldiers return and have a difficult time adapting to civilian life.  All of the areas of public policy that touch our societal arrangements could reasonably be said to be social policy.