I know that a geographic coordinate systems are inherently three dimensional, while they are usually represented by two coordinates (lat and long) because the height is about the same across the surface.

These 3D coordinates are eventually projected to a 2D screen when we use a GIS software. My question is doesn't that mean they are practically projected? Isn't the only way a coordinate system is geographic, and not projected is that the map information is on a 3D sphere (like on a physical globe or Google Earth) and not on a 2D surface?