When moving a face, items are moving that I didn't select. What's happening?
When performing a Sychronous Edit, we display "Live Rules" controls at the bottom of the screen. These allow you to control how faces associated with the select set move. For example, Co-planer looks for all the faces that are in the same plane as the face you are moving . . .and moves them with the selected face. Turning it off, would ignore those faces and leave them behind.
The same goes for "Concentric". There are also controls for symmetry, Dimensions and a few other things. Some expiramenting should help understand the relationships.