For example in car racing, the non-straight parts of the track are almost always called corners, even though many of them are very far from the typical (point-like) corner of a rectangle.
Merriam-Webster gives the following relevant meaning of curve
a smooth, rounded line, shape, path, etc.
and the following meanings for corner
1) the point or area where two lines, edges, or sides of something meet
2) the place where two streets or roads meet
3) a curve in a road
This suggests that the two are in principle interchangeable, although I suppose that corner goes back to point-like intersections, whereas curve is more appropriate for extended intersections.