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In the old days, pre-2020, "playing to your handicap" meant a net score about equal to the Course Rating. that led to problems when people played against each other from different tees, people playing tees with a lower CR would generally shoot lower scores. Course Handicaps were adjusted for each competition to make it even, usually lowering the course handicap for the "forward tee" players. So now if you "play to your handicap", the (68.4-72) term means your score will be even par, no matter which tees you play from. No adjustment needed for people playing from different tees. Look at your example, the guy shoots 82 every time, his Course Handicap of 10 gives him an even par net score every time.
Because of the 68.4-72 part. If he shoots 10 over par (his course handicap), he will have shot his index.
You don't factor par in when you calculate the differential, but you do when you calculate the course handicap. That's where the difference comes in.
It works symmetrically: guy shoots 82 and gets a 12.4. Guy plays off a 12.4 and… has to shoot 82.
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