What is the difference between a Handicap Index, a Course Handicap, and a Playing Handicap?

Why do I see different numbers for my handicap?

A Handicap Index can be thought of as the player's "raw" number, as calculated nightly and denoted by a decimal figure; i.e., 15.2. This value represents the player's best demonstrated ability based on their current scoring record. However, the player never actually plays golf with this number; rather, it must be converted to the Slope Rating of the tees that are being played to a whole number in order to be used. This conversion is called a Course Handicap and represents the number of "strokes" the player needs on that tee set. When the player enters a competition, the Committee in charge may adjust the Course Handicaps of the players due to a condition of the competition such as a format of play that reduces the CHs (referred to as an Allowance - i.e., Four-Ball Stroke Play allowance is 85%) or an adjustment to the players for a difference in Pars between tees played. This is called a Playing Handicap.