That is a good question!
Based on my experience, set extension is just an act of extending your set in post, and that can be achieved by using matte painting.
As for your second question, I believe there are 2D, 2.5D, and 3D extension.
2D Set extension, is usually just 2D matte painting layered on the background.
2.5 set extension, is projecting that 2D Matte painting to simple geometry (to simulate parallax),
and then 3D set extension, which is creating the background extension with a fully 3D scene/model
That is just based on my experience, feel free to correct me if i’m missing anything!