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.
They move in ellipses on earth as well, but it’s cut short by hitting the ground. Also, air resistance affects the trajectory so that anything thrown/shot will eventually return.
Source: Thousands of hours in KSP