Mapping Center Answer:

Some map projections support only spheres while other support both spheres and spheroids (sometimes referred to as ellipsoids). If a map projection supports spheres only, but the geographic coordinate system is spheroid-based, we use the semimajor axis for the radius of the sphere. This adds distortion to the projection. The sphere-based folder contains definitions using a geographic coordinate system that uses a sphere definition. The sphere is what’s known as an authalic sphere. It has the same surface area as WGS 1984. Here is a help topic that relates to this discussion: Spheres and Spheroids.