A system for making wallboard or backerboard sheets may include a mixer for mixing materials for making aerated concrete, at least one face layer supply, and a former downstream from the mixer. The former is for forming core material having opposing first and second major surfaces and comprising aerated concrete, and for securing at least one face layer from the at least one face layer supply onto at least one of the first and second major surfaces of the core material. The system may also include a cutter downstream from the former for cutting the core material and at least one face layer secured thereto into a plurality of wallboard or backerboard sheets. The provision of aerated concrete for the core provides many key advantages over conventional gypsum wallboard sheets, and/or conventional backerboard sheets, such as gypsum greenboard or cementitious backerboard, for example. In one class of embodiments, the former may further include an autoclave for curing the core material prior to securing the at least one face layer thereto. In another class, the former may further include an autoclave for curing the core material after securing the at least one face layer thereto.