Exactly. A programmer is a line cook. You want to be thought of as a guy who has potential to be a Chef or is one. I think the whole "impact of your work in numbers" also dovetails into this. That changes you from being an interchangeable cog to someone who can bring value and change the company.
While it might make one feel better to call oneself an engineer (you're not, it is not one of the original engineering practices), a developer (I guess, is it any better though), guru, ninja, evangelist (rebranded words). There is absolutely no need for these names in the software context. All of these words are made for the touchy-feely Gen-Y'ers (which I am a part of). While everyone tries to make the word "programmer" a dirty word these days, I'm proud to call myself one. When I go into job descriptions, I would put "Helped architech...", "developed a...", "designed flow of...", and etc.
I would argue anyone that is creating anything within software is doing engineering (and know what they are doing):
The American Engineers' Council for Professional Development (ECPD, the predecessor of ABET) has defined "engineering" as:
The creative application of scientific principles to design or develop structures, machines, apparatus, or manufacturing processes, or works utilizing them singly or in combination; or to construct or operate the same with full cognizance of their design; or to forecast their behavior under specific operating conditions; all as respects an intended function, economics of operation or safety to life and property.
Software engineers take scientific methods created/researched/etc from Computer Scientists and created something from it. The difference between an engineer and joe shmo is that an engineer understands the science behind what they are doing.
An engineer could build a bridge and a regular guy could build a bridge. Both may work for 100 years, but the engineer KNOWS it will work for 100 years (under specific conditions obviously) and the regular guy doesn't. The same could be said for software.
While I do agree with you somewhat, I'm willing to give up to be called an engineer by others to stop all of these new engineering disciplines from appearing: political engineering, social engineering, market engineering. With this logic you can apply engineering to anything you do. Engineering used to be a much nobler and much more respected calling, not so much anymore.
Agreed that there is really no distinction in most cases (software engineer = software developer = programmer = guru = ninja etc), but it matters to the people in positions to hire you. I bet someone with a job title of 'software engineer' is perceived to be more 'prestigious' even if the job is really the same.
I am sick of job ads that use words like 'ninja' and 'rockstar', btw.