I have a friend who's more like a civil engineer. She's the sort of engineer who approves the architect's plans to confirm that the building or bridge won't fall down if it's built the way they say it will be built on paper.
I used to work for the Engineering department of a major city (in a secretarial capacity). Most of our stuff was roads. We worked closely with Transportation/Public Works, though, for things like bridges, highway improvements, tollroad projects, Capital Improvements Projects, things like that.
One NASA engineer I know used to be a nuclear engineer for the Navy, then was a nuclear engineer in civilian life, then went and got his MA/PhD in aerospace engineering. He works with space radiation analysis. Pretty much everyone else in his area is an MD, but the skills he relies on are more in terms of things like pattern recognition and SuperMath.
I know maybe three or four other NASA engineers in my circle-o'-friends, but I haven't talked shop with them as to what they do with their day jobs. I only know them by their hobbies.
But when I think NASA engineer, I think "math", perhaps because JSC is what I think of when I think of NASA. Someone who's based out of Kennedy would have a different skillset than someone who's based out of White Sands. Someone who's at JPL is likely to have a different skillset than someone who's at AFRC.