And as to why there are so many variations, it keeps things interesting and allows for different strategies and different strengths. Excuse the EC nomenclature in my explanation here:
Some horses do well with an immediate (i.e. stopping after your first round but staying in the ring to proceed to your jump-off) jump-off while others do best having some time to rest and regroup with a special warm-up specifically for the jump-off. Immediate jump-offs allow the show to run more quickly while the delayed jump-offs make for a more interesting event for the spectators, as well as making it easier for the riders to determine what they need to beat (therefore grand prix classes are always a delayed jump-off).
Power and speed courses are longer, so some horses will have an easier time with them than others. There’s a different strategy involved in transitioning mid-course from one type of ride to another. They also run really quickly when it comes to the show schedule.
Table A speed (no jump-off) is an entirely different strategy altogether because you have to go quickly without having ridden those jumps in advance with more generous turns, You also must keep the jumps up so you can’t go too crazy with the speed, but you also need to try to be the fastest clear.
Table C speed allows a different strategy altogether since you can make up for a rail by going quickly. This allows you to take more risks and you can go in with more confidence on a horse who isn’t quite as careful as some others.