The funniest part of this article (in the context of being posted on HN) is that the author separately mentions engineer and software engineer in her list of client professions. That settles it - normal people think they're different.
https://www.hillelwayne.com/post/are-we-really-engineers/ (first post, later ones linked from the top)
But perhaps most importantly, I think we all know (right?) that the title Software Engineer is not, in practice, currently imparted consistently with how much “real” engineering is being applied.
https://www.nspe.org/resources/pe-magazine/may-2018/ncees-en...
There is no certifing body (in most countries) on who can call themselves engineers unlike doctors or lawyers.
So it is really up to you , whether you see what you do as engineering (not only with software) or not