"Developer" is a word that requires some context. A stranger might not know if you worked in construction or on computers.
On a professional context I'll say I'm a software developer. If I want to brag a bit I'll say I'm a software engineer. If I'm with friends I'll say I'm a programmer. If I'm with family or older people I'll dip my toes with "I work with computers" and maybe further explain if prompted.
I just say Software Engineer its what my employer calls me and resolves what I want to call myself.
This is much more entertaining when you have family who are PEs and their eye twitches every time.
Which is funny because there's also backlash against Computer Science that it is not in fact a science, which is why they added math courses to some degrees, at least here in Florida. I think Computer Programming is just probably best described as Computer Programming but I do like saying Software Engineer every time someone asks just because it sounds good enough to me. Until they standardize our title into one single thing, I'll just go by SE.
Funny, where I come from the earliest computer science departments at universities where basically joint ventures of the maths and electric engineering departments. Consequently they were quite maths heavy, and it shows to this day.
>and maybe further explain if prompted.
I write manuals for computers.
"So, like, for how to use them?"
No, the computer reads it so it knows what to do.
Holy shit, are you me? I do the exact same thing. I literally say "I build websites" while typing on an air keyboard.