Anything that changes the energy of the structure is a move. Each sidechain you substitute with Mutate, therefore, is a move. Each change of a rotomer from one position to another is a move.

Unfortunately for scripters, each rebuild or remix is a move. Some scripts rebuild a single segment range forty times in just one pass.

Changing a loop to a helix via the Blueprint tool is a move, but changing a loop to a helix through the structure mode is not. The first physically changes the structure, and therefore the energy, whereas the second just changes the visualization of that structure.

Undoing a move counts as negative one moves.

To be honest, counting moves is not a effective way to induce producing better quality results. Mutate, rebuild, and remix are essential to fix bad loops and improve sheets and helices. Why prevent us from using them?

I look at it this way: Anything that is required or helpful to create or design a protein cannot be a move. Or you would have no fold, no protein.

You can say that wiggle and shake would not be a move by that criterion but here's the thing. You can fold a perfectly designed protein without ever wiggling or shaking. The energy score may not reflect what would happen when the protein interacted with itself and its environment, but it's a complete design, ready to go. A prototype if you will. Wiggling and shaking will test the design; but used too much they are the source of seeking a high score rather than designing a viable product.

Similarly you cannot design a protein withou mutating (unless you just want all leucines, etc). Banding and blueprinting might not be considered a move because you can design without having to band or use the blueprint (which are often only useful as an shortcut) but they are an aid to "folding," as are cutting, uncutting, and pulling. Not really different from translating, rotating, zooming etc. And many of these change the energy but without them there is no design.

Wiggle and shake are the only things that set the protein fold in motion. And this is what should be targeted by the move limis if we want to curtail score seeking, but not protein designing.