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If they are the same shapes but differ only in size, then they are SIMILAR shapes. Otherwise, they are simply different shapes.
They are said to be similar shapes and have the same interior angles.
A cube has 6 flat surfaces. Most boxes of all shapes also have six flat surfaces
Sphere, ellipsoid, torus, paraboloid, hyperboloid are shapes with only curved surfaces. Hemisphere, quadrant, cone and cylinder are examples of shapes with curved and plane surfaces. There are, of course, many others.
Yes - even shapes with different area.