Surprising that no one in this thread has mentioned education as an additional distinguishing chracteristic. Programmers are frequently self-taught. If PG essays and HN submissions/comments are any indication, many programmers dislike school. It is said that programming only requires very basic math skills. There are requirements on professional engineers that do not apply to programmers. Engineering, in the US at least, is generally a regulated profession. That's the point of difference, irrespective of whether programmers perform similar work.
NB. When I use the term "regulated" I mean there are licensure requirements. For example, an exam.
https://www.nspe.org/resources/licensure/how-get-licensed
https://ncees.org/exams/fe-exam/
https://www.nspe.org/resources/pe-magazine/may-2011/industri...