I think programmers focus on aspects of the program - like memory optimisation, speed, accuracy, correct data processing, storage, database optimisation, etc. Good software engineers focus on aspects of the system as a whole - like the technology with the best memory optimisation, fastest filesystem, most suitable database, etc.

Engineers look at the big picture as a whole, programmers make sure the detailed aspects of it are working in the best possible manner.

For example, a good programmer will tell you to never use nested for loops, but an engineer may go for it nevertheless, if he feels that there is not much difference in the speed and memory consumption. He will make some tradeoffs depending on different factors.