Foursomes (Alternate Shot)
A team format where two partners share one ball, alternating shots (and alternating who tees off) throughout the hole.
The official Rules of Golf name for this format is "Foursomes," alternate shot is just the common casual name. It's the format used for half the matches at the Ryder Cup and Presidents Cup.
It rewards a different skill than stroke play: since both partners have to play whatever position the other one leaves them in, course management and leaving your partner a comfortable next shot often matters more than pure ball-striking.