Could you explain why the resulting country shapes are so different? Is one of them "more correct" than the other in regards to what you'd see if you were floating above the earth?

Neither are "correct" in mimicking a 3d view floating above the earth because both are 2d representations of a curved 3d surface. The left view maps longitude and latitude directly to the plane which results in shape being distorted. The right view, using a form of transverse Mercator projection approximately preserves shape so is closer to what an orbiting viewer would see. For more on how map projections affect shape, see https://observablehq.com/@jashkenas/interpolating-d3-map-projections

Ah, that makes sense. Thank you!