It's actually more that an SDET has classically been the one who writes the tools and infrastructure that QA Automation Engineers would use to write scripts.

It implies an education/experience background equivalent to any other T&I Software Engineer, but usually with additional experience in QA. Alternately, it could be a QA engineer who would be genuinely qualified as a general SWE in a promotion path, but who chooses to stay in quality as a domain. But either way it implies equivalent qualifications as a SWE at the same level.

The "real" bit is because over the last half decade or so, SDET has been blurred by title inflation. Scripters have been getting the title without any real experience maintaining longer-term or larger software projects, and who aren't qualified enough to be hireable as a SWE generalist.

That's one reason you still get "lesser than SWE" status arguments about SDET, when IME you actually tend to demand a little more in the market because of the need for experience in two separate disciplines.

My response to the comment above you has a lot more detail expanding on that.