A spherical coordinate system projected onto a flat map is called a polar coordinate system. The entire azimuthal angle information is lost in the projection. The only other option is to distort the image to preserve the azimuthal information, which results in scale distortions.
This is exactly what happens when a globe is flattened onto a 2D map, Greenland is the notable example of distortion.
Longitudes and latitudes have no existence on a 2D surface - we just call their replacements the x,y coordinates. In spherical coordinates, they count equal measures of polar and azimuth angles.