Stroke Play: The style of play where each player (Individual) or each partner (Foursomes) plays their own ball.
Match Play: The style of play where one player or side (Foursomes) competes against another player or side for the number of holes won, not total score. A player or side wins the match by being Up more than there are holes remaining. Example 2 and 1 (2 up with 1 hole to play).
Net Best Ball (BB): Typically scored as 1 Net BB of the 2. Two players per team and both players play their own ball but only count the 1 Best Net Score. Also played with 4 person teams and count the 2 Net Best Balls.
Alternate Shot: Two golfers play as a team and alternate hitting the same golf ball. Also a Modified version where both players tee off and choose the best drive, then the other player hits the next shot and alternate from that point.
Scramble: The best of the tee shots is selected and all players play their second shots from that spot. The best of the second shots is determined, then all play their third shots from that spot, and so on until the ball is holed. Can be 2 or 4 person teams. Sometimes handicaps are applied in Scrambles to level the playing field such as an ABCD Scramble.
Stableford (Quota): A Stableford competition is a golf tournament in which the object is to get the highest score. That's because in Stableford, golfers are awarded points based on their scores in relation to Par for each hole. Here's the point breakdown:
Hole in one: 10 points
Double Eagle: 10 points
Eagle: 8 points
Birdie: 4 points
Par: 2 points
Bogey: 1 point
Shamble: Like in a scramble, all members of a team (usually four) tee off and the best ball of the four tee shots is selected. All players move their balls to the spot of the best ball. From this point, the hole is played out at stroke play, with all members of the team playing their own ball into the hole.
Flag Tournament: An individual event where each player is given a flag with their name and handicap info attached. The object is to go as far as you can around the golf course within your allotted strokes. When all of their strokes are used up, the player plants his flag in the ground where he finished. If a multiple players finish all 18 holes and have strokes remaining, they will go into a shootout using their remaining strokes to determine the winner.