This is the family of Tafl games. Characteristic of this game are asymmetrical game play, custodial capture and winning either by getting a particular piece to a corner or side of the board or for the other player by capturing that piece. Additionally, the sides are that special piece, plus x defenders, against 2x attackers.
Hunt games - Each side has only one kind of piece. Also there are typically very few "hunters" and many of the opponent pieces.