In a “Scramble” format the players or designated team captain decide after each shot which one the best shot is. Each player on the team plays their next shot from that spot; within one club length no closer to the hole. 
The group then plays this way until the ball is holed out. The group takes a score at the end of each hole based on the single best shots from each position on that hole. Some of the factors are longest drive, best position for approach shot, easiest putt, etc. So in other words if Player A hits the better drive, Player B picks up and goes to the Player A’s drive and hits from there. If then, Player B hits the closer iron shot to the pin, Player A would play from Player B’s position on the green until the ball is holed out. Each person on the team gets to hit from each position. Scrambles are more popular in corporate events where handicaps are not a concern; you are there to win, but have fun at the same time.
In a “Best Ball” format, each player plays their own ball throughout each hole. The team’s score for the hole is the lowest score shot by a single team member on that hole. So in other words, if Player A and Player B are again partners and one makes a 4 and the other a 5 with their own balls respectively, then the group takes a 4 for that hole. Handicaps can be used in this format to make it more fair for everyone. This format is a little more serious as everyone gets to play their ball for a full 18 holes; usually for the more serious of golfers.
Hit it pure!
Justin Rubenstein
VIP Golf Services
President/CEO/CFO