What are Local and Global Inpainting Techniques in Image Processing?
Usually one could divide the methods according to:


Global Method
The function optimized is all over the image with no local data.
Namely it finds best solution involving all pixels.
Diffusion Based is usually iterative method to solve such a Global model.
Local Method
The optimization function is local for a group of patches and holes.
Most "Patch" based methods are local in their nature.


In practice, state of the art methods combine both approaches.
Namely global regulator over a local optimization function or the other way around.