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.
Basically, it’s an ellipse on Earth too. Just one that’s nearly a parabola. Because of approximately constant gravity and an approximately (approximately!) flat Earth, like the current top commenter said.