Considering the almost complete lack of standards, certification, licensing in most areas of programming, I don't think there's a ton of difference.
I've held both titles without rhyme or reason between the two. Even in areas requiring high compliance - HIPAA, PCI/DSS, NIST Standards, FERPA, etc - training achieved doesn't tend to be reflected in a programmer's title. (Even while the same level of training turns into acronym soup among their IT peers.)
One way I try to live up to the title "Engineer" - even when I don't wear it - is by holding myself to the Engineering Code of Ethics.