Research plan vs proposed research for class project?
In general a research plan will include within it a section that deals with the proposed approach. As this University of Michigan page explains:


  Research Plan (Approach)
  
  This section includes a comprehensive explanation of the proposed
  research, and is addressed to other specialists in your field (not to
  laymen). The section is the heart of the proposal and is the primary
  concern of the technical reviewers. To make it clear and easy to
  follow, you may need several subsections tailored to your work.
  Research design is a large subject and cannot be covered here, but a
  few reminders concerning frequently mishandled aspects of proposals
  may be helpful.


As always, you should talk with your advisor/professor to ensure if this is exactly what they have in mind, or if there is some specific template or example for your field/subject/use that you should follow.