Why is AO considered Post-Processing?
This is a potentially confusing re-use of terminology. Ambient Occlusion is not in itself a post processing effect. Screen Space Ambient Occlusion is a post processing effect using the depth buffer to approximate the effects produced by Ambient Occlusion.

Ambient Occlusion is a relatively expensive global method, while Screen Space Ambient Occlusion is the cheaper alternative for real time animation. Only the latter is considered post processing.