My wife and I won the "Divorce Open"- excuse me, Couples Championship, net division, at my former club playing the Chapman or Pinehurst variation of foursomes:
"This 2-person team competition format is named after Dick Chapman, a great amateur golfer who played The Masters 17 consecutive years. He "invented" the game at Pinehurst Resort, hence it is alternately called Chapman or Pinehurst. And, for good measure, it is less frequently referred to as American Foursomes.
In the Chapman System, both players on a side tee off, then they switch balls. Player A plays Player B's drive, and vice-versa. Each player hits his or her second shot. They then select the best of the second shots, and from that point until the ball is holed they play only one ball in an alternate shot format."
The club also had a true foursomes for 9 holes in a 27 hole match play Ryder Cup style event.
I've never played true foursomes in a casual round.