Quite right. If you think back Dave to the old days, there was lots of engineering going on in order to actually get recordings “on tape”. So basically the job of engineering was very broad and encompassing, and involved the setup of tape machines, calibration, tape inventory, hardware prep, manually resetting the console from the last session (if it hadn’t been already), getting an intern or asst engineer to make notes and diagrams of the new project (both pre and post), routing of mics and instruments for the incoming session, mic choices, drum and amp mic setup, experimentation if the band was avant garde, sound check run-throughs, actual session recording, tape unload and storage, band consulations, producer consultations, etc.
While many of those steps apply today, excepting the tape machine and blank tape (usually) and solely hardware gear, things tend to be a bit more streamlined and compact these days. Including those “roles” in which now a single person might record, mix, and master a whole song or record. There is not the record industry budget and staffing in many cases, so a lot of it is solopreneur engagements.
This allows for one person to engineer, produce, mix, master, and even handle A/R stuff like marketing and promotions for artists - if they so choose.
IMO, this mentality shifted sometime in the 2000’s, from the old terminology to newer ones. At least in what we called ourselves. So the overall term could be Audio Engineer for any of these roles. The old term of Recording Engineer still stands for “tracking” duties", but isn’t used that much. I think Mix Engineer is a relatively new term, and has emerged as an exclusive and ‘boutique’ role that one person may specialize in. Remember, with old consoles and tape, especially before automation and recall, it might take 6-7 people to mix down a song in “real time” with basically assholes and elbows turning knobs and pushing faders according to a rehearsed mix strategy! The guy in charge of that team would have got the credit for “mixed by”.
The job of Mastering Engineer used to be a select elite few, like Bob Ludwig, who appears on virtually every old record in my collection. These guys were ultra specialists and were contracted by the record companies so it was kind of a monopoly. The digital scene changed all that, and now anybody with Ozone and a bit of knowledge can at least pretend to be a Mastering Engineer.
Digital turned the whole industry on its head, but also liberated music making to the masses.