I spent 4 years getting a degree in mechanical engineering while also working full time as a Manufacturing Engineering Technician (my company wouldn't drop the "Technician" in my title until I had the degree, even though my duties were the same). After I graduated, I got a job with the title Product Engineer, which was essentially mechanical engineering.

When I moved over to the software world, I didn't really notice an appreciable difference from the work I was doing when I had "engineer" in my title. You're still solving complex problems, accommodating for edge cases, and translating requirements into deliverables. The only differentiator is that I went from producing something physical to something digital. So I call myself a "software engineer" without really thinking about it. Nobody ever blinked an eye when I said I was a mechanical engineer. Nobody dug into whether I was accredited or licensed. One could argue that distinguishing between a programmer and a software engineer is analogous to a drafter vs a mechanical engineer, but that seems wrong too. At the end of the day, you can call me whatever you want as long as the check clears.