Shades of the 1980s and prior decades! In the 1980s, I worked in the aerospace division of a Fortune 5 company. A headhunter called me up, was chatting, and asked me what I did. I said I was a "programmer". Silence on the other end and then, "Are there any people who design programs there?" "Umm, yeah, we all do." I was book-aware of this distinction in previous decades, but this was the first time I had encountered it in the real world (of a headhunter). I see that we "programmers" are still regarded as being like the streetsweepers in Victorian London, sweeping out a path in the manure and mud for the software engineers! :) (We had software architects back then.)

I don't know if you can really make the distinction, is anyone actually hired as a "programmer" instead of an "engineer"?

I feel like developer is the best name for what we do, it doesn't limit us to the act of coding and it doesn't make the presumption we're engineers (very few of us actually are).

Then again if I could choose I'd probably prefer computer programmer, it doesn't get confused with property developer and pretty specifically covers what we do.

That's a reasonable way to look at it, but there is a missing component. In the early 1990s, I was a subcontractor at a large firm which had software people who were only interested in designing software, down to a medium-level pseudocode, after which the design was handed off to coders. These designers were great people, but, on this project, none of the firm's designers and coders had hands-on knowledge of and experience with the hardware and operating system (an early version of VxWorks). The coders would gain this knowledge and experience from writing and testing the software, but not so the designers.

My missing component was that there was no mind-to-mind feedback loop conveying this knowledge and experience gained by the coders back to the designers, from which it would inform the designers' future designs. (And there was no regular feedback about how well the design fit the problem and if the design required radical changes during coding and testing, although some of that is more an administrative concern than a technical one.) The "coders", by the way, were quite capable of designing their own programs - and did. I don't know why the firm had this subset of design-only'ers; they were smart and maybe the firm wanted to hang on to them and maybe "coding" roles were intended for brand new employees.