So of course both of these are slight simplifications, but what is the connection between the two? If the earth is basically a circle, is an ellipse just a parabola stretched around a circle? Is a parabola just an approximation of a tiny part of an ellipse? How high do you have to be before you change your calculations of a trajectory?
The Math ain’t mathing.
Only stable orbits are elliptical. Many objects follow parabolic and hyperbolic trajectories in space. Eventually, many intersect with other objects. As time passes, objects that are not in stable (or semi-stable) orbits become less common through attrition.