CAE may actually involve no graphics. Think of FEM with punch card input decks . CAD/CAM is full integrated CAD/CAM, unlike these CAD-only systems. It often can include CAE.
CAM usually involves good process engineering. Nothing is actually "automatic to production" in most cases.
I'm amused with the actual "work product" of these new-fangled CAD systems. Paper prints. We used to think 3D models and actuual produced 3D product ... perhaps they just became too "easy to use".
HTH