What is the difference between a "research plan" and a "research proposal"? Online sources often use "research plan" and "research proposal" interchangeably.

Two months after getting accepted into a PhD program, I was asked to do a research plan.  Is this the same as doing a research proposal?
Neither a research plan nor a research proposal is a "super specific thing you need to know about".

A proposal, on any subject, generally includes things like objectives, background, potential challenges, and a vague schedule.

A plan often includes all of the above, in greater detail, as well as necessary resources, a specific schedule with milestones, and perhaps additional project specific elements (e.g. which programming languages you might use).