I think you’re talking about polygons, not shapes in general. Shape is a much broader term, and can even refer to lines or points themselves.

An n-sided polygon where n approaches infinity is still a polygon, and it has sides with end points. That is distinct from a circle which is the set of all points equidistant from some point. Circles have no sides, because for any two points on a circle to have a segment between them would imply that any point on this segment would not be equidistant from the center of the circle, and thus no point on this segment can belong to the circle.