Since I'm from visual arts field I can try to answer this one.
Don't know about US but in Europe Arch is strongly connected with fine arts. In my country you need to pass entrance exam which is: drawing a model, drawing a still life and ofc an architectural drawing. You need to have A-levels in math and physics too.
Arch degree is a mix of fine arts courses like drawing, painting, photography, sculpture, typical civil eng courses like materials, structures and mechanics and typical design courses like architectural design or urban design.
Civil Engineering degree is a mix of science courses like math, physics and chemistry, cilv eng courses like materials, structures and mechanics (but you have it much more than in arch) and geo, hydro, thermo and soil stuff. You have also many technical drawing courses.
Both degress are heavy on "bureaucracy" courses.
So more or less an architect is a designer - someone who comes up with nice looking and functional building and civil engineer is.. an engineer - someone who ensures that architect's design will be build properly - useing proper materials, proper construction etc.
Hope that helps.