Plated half-holes PCBs ,it also called castellated holes are used for board-on-board contacts, when two printed circuit boards are mixed with various technology. E.g. the configuration of complex modules of microcontrollers and typical individual PCBs.
Through holes on a PCB means a hole that is drilled from the top and through to the bottom of a PCB, these can be plated (PTH) or non-plated (NPTH).