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.
If something is moving in an elliptical orbit, and you are observing it from a fixed point in space, it will appear elliptical.
If something is moving in an elliptical orbit, and you are observing it from a body that is itself also moving in an elliptical orbit, it will appear parabolic.