A differential pressure application apparatus is configured to apply different amounts of pressure to different locations of a substrate, such as a semiconductor device structure. The apparatus may be used during polishing or planarization processes. The apparatus includes pressurization structures that may be moved independently from one another. An actuator may control the amount of force or pressure applied by each pressurization structure to the surface of the substrate. Systems including the pressure application apparatus, as well as differential pressure application methods and polishing methods are also disclosed.