Definition of 'Charity Ball' in Golf
A charity ball is a golf ball that your playing partners tell you to drop in order to replay a stroke because you just messed up the stroke so badly they feel sorry for you.
A mulligan (also called a lunch ball or Sunday ball) is a do-over — a replay of a poorly struck shot that a golfer claims without penalty. (Needless to say, charity balls, mulligans are not allowed under the Rules of Golf, but we're talking here about things that happen in casual rounds between golf buddies.) Groups that use mulligans typically have certain rules, or at least customs, that they abide by. For example, your regular group of golfers might allow mulligans off the No. 1 tee only; a different group might allow one mulligan per nine.
"Charity ball" can be used a synonym for "mulligan." But the charity ball usually comes without any of those customs of use. A charity ball is more often a spontaneous thing that your golf buddies urge on you.
Let's say you are trying to reach a green up ahead, and your approach shot has to clear water to reach that green. So you take a swing and, oops, your ball just plopped into the water. You follow the rules in taking a drop and applying the penalty, but, whoops, you do it again — another ball in the water.
At this point, if your buddies aren't laughing too hard, one of them might say, "Just take a charity ball." They are urging you to take another ball out of your pocket, drop it, and play the stroke again. But they aren't expecting you to go to the drop zone or apply the penalty. (That's the charity part.) They just want you to take another shot at it so that maybe you'll get it right this time.