Course handicap vs playing handicap
Your Handicap Index travels. The strokes you get today do not. The course handicap turns the index into strokes for a set of tees. The playing handicap then trims that number for the format, so a stroke-play field and a four-ball are not handed the same card.
Course handicap
Course handicap = index × (slope ÷ 113) + (course rating − par). Slope 113 and a rating equal to par give you a course handicap equal to your index, before rounding. A higher slope, or a rating above par, gives you more strokes. You need the rating, slope, and par from the tees you will play. They are printed on the scorecard.
Playing handicap
Playing handicap = that unrounded course handicap × the allowance, rounded once at the end. Individual stroke play, Stableford, and par or bogey are recommended at 95%. Individual match play is 100%. Four-ball stroke play is 85%. The allowance is applied before the final rounding so a player is not rounded twice.
Which number goes on which hole
In the competition, strokes follow the playing handicap and the stroke index. Stroke index 1 is first. When you post a score for your index, the hole cap is net double bogey from the course handicap, not from the 95% playing figure: par + 2 + strokes received on that hole.
Nine holes use half the index and the nine-hole rating and slope. Do not invent them by cutting the 18-hole numbers in half unless the card says that is correct.