Rhetor v. Rhetorician

I have a question for you, Ars Rhetorica.

Recently, I was talking with someone about the differences between studying rhetoric today versus studying rhetoric in ancient Greece. This person doesn't study rhetoric and was confused about whether I was studying rhetoric to be a good communicator, debater, persuader, etc. I clarified by making the following distinction:

That's the difference between being a rhetor and being a rhetorician. I'm a rhetorician, someone who studies what rhetors do.

Is that
a valid distinction? (I have no shame about being wrong, so feel free to say you don't buy the distinction. If you don't buy it, just give me a good reason why so I can know why I shouldn't buy it either.) There are the obvious caveats about rhetoricians' having to communicate their ideas, and aren't we all ultimately rhetors, etc. But aside from that, what do you think? Are the two terms interchangeable nowadays? Is "rhetorician" just a silly, academese way of talking about "one who studies rhetoric, which, by definition, includes rhetors"?