Hi Andrew,
Convert To Mesh Applies the Modifiers on the Cube, it doesn’t remove any Cutters.
There is indeed a difference in the Bool Tool, as it now also Parents the Cutter to the Object (as you can see in your Outliner), that is why the Spheres move with the Cube.
That you can’t see the ‘holes’ in the Cube in Edit Mode is something that I can’t understand.
