'Shift' tends to imply a small movement or adjustment. 'Move' typically refers to a greater change in position.
If I shift a picture to the left, I might only move in a few inches. If I move a picture, I might be changing its position entirely.
Changing houses is a substantial effort, so we use 'move'.
However, you can say a house shifts. For example, if I say "The house shifted on its foundation.", then the house is still in the same location, but due to some kind of problem, the house no longer sits squarely or firmly on the foundation.
