Board-to-board connectors which connect to PCB’s side-by-side are called coplanar connectors.
Board-to-board-connectors which connect PCB’s ontop of one another are called mezzanine or stacked connectors.
Wire-to-Board (WTB) Support
Some board-to-board connector families are have wire-to-board support, with a special wire-crimped inline receptacle which mates with the PCB-mounted connector that works with both the board-to-board and wire-to-board connectors.
The Hirose DF-59 family is a set of board-to-board/board-to-wire connectors. The special feature about this family is the “floating” contact which allows up to 0.5mm of mis-alignment between the boards.