2D Plane Stress calculates Normal stress in 2 directions: Global X and Global Y and assumes zero stress in the Global Z direction. If you make a Cylindrical Coordinate System for a circular object like a ring in the XY plane, you can make Radial (X), and Tangential (Y) directions.

Axisymmetric calculates Normal stress in 3 directions: Radial (X), Axial (Y) and Hoop (Z). It does not assume zero stress in the Axial direction.