Maybe visually this will help: I drew over the two images I posted above, where the triangles and squares could possibly be. This is not their exact locations, but it is reasonably accurate for illustrative purposes.
2D castle - showing how it's composed of non-oriented squares, with images applied to those squares. I used a different color for different squares, to make it easier to see. One square is a single image draw by an artist, and the shadows and curves are drawn into the square image.
See how I have the tower as a single square? It's probably one image. Maybe two: the tower and the tower's roof. The banner on the towers look like a separate image. Some 2D games, like my own, use only images of a specific size, and let map makers recombine the images (called 'tiles') to build the world.
3D castle - showing how it's composed of oriented triangles with images applied to the triangles. The shading/lighting is calculated by the nature of it being 3D. To make curves, you just use more triangles to make it look smoother (see the archway) or the base of the tower roofs).
I didn't bother drawing every single triangle - and often the really large triangles will be broken into a few smaller ones - but not many small ones.