This is not true at all, except maybe in very specific places (e.g. some jurisdictions do not allow you to call yourself an engineer without a specific qualification).

Software Engineer and Developer are essentially interchangeable terms and largely a matter of taste.

Eh, as someone who's first software job was as an "Associate Software Enginner" while still in school (undergrad), I'm pretty sure I can say it's not that cut and dry. I've actually never had a software job that didn't use the "engineer" title. I've found "developer" and "engineer" are used interchangeably.

this seems to reflect the simultaneous co-opting of the titles "architect" (one who designs physical edifices such as buildings) and "engineer" (one who applies math and science principles to problems of infrastructure and industrial production). We all understand what is meant by design, but that does not mean a software design must be devised by an "engineer" or an "architect" anymore than an interior design (though there are also some self-styled "design architects" roaming about). So is it possible to say what is different about software development and software engineering without saying the engineer is an architect? Is it that software developers do not design anything (which in its simplest terms is 'artful arrangement')? That seems arbitrary - though I agree that there can also be a fine line sometimes between, say, architecture and structural engineering.