Hi Daniel,
The two phrases are not interchangeable.
The Project Management Plan as you say includes all the sub-plans, tools and techniques, etc.
The Project Management System is a way of using the tools and techniques to manage the plan, for instance Microsoft Project is a type of Project Management System, although incomplete for a whole system, it can help you manage your schedule, and costs. The system is a tool, so can be part of the plan, by the plan is never part of the system.