That is a great question, and I will give my opinion here.
A staffing plan is part of the project management plan to help properly staff and manage various project teams. These plans usually include staff acquisition timelines for how long staff is needed and their release, identification of any staff training, team building strategies
The human Resource Management Plan tends to describe how the human resources are to be defined e.g. roles, responsibilities, reporting structure etc. This is intended to cover the whole project. It is a process of large scope which includes creating a staffing management plan. This plan will, or should contain a roles and responsibility description, organisation charts, and a staffing management plan.
So, they are related, but not the same scope i.e. the SMP is specific scope whereas the HRMP is the overall strategy.
Ithink earlier editions of the PMBOK do a better job of explaining this then the current version.