Trap and skeet are for ill tempered "old farts", who can't move well ..... or fast ..... whose eye sight isn't the greatest, so they have to have targets flying on the same flight paths in open areas. It can get as monotonous and boring as heck ......... really quick for me. LOL LOL
You can probably tell already, where my preferences lay. LOL
Sporting Clays is, unless you have a golf cart to ride, a game for a more vigorous shooter, who isn't annoyed when someone drops a shell on the ground, talks behind him or makes jokes as the shooters get ready to call for a target. Except during serious competition, sporting clays is a much more relaxed fun shooting game, more closely duplicating the shots most of us actually see in the fields, and marshes, any more.
But, it is more expensive. Around here a 50 bird round of sporting clays is $15 - $18. A round of 25 birds on a trap or skeet field is about $3.50, about 1/3 to 1/4 the cost, per bird, of sporting clays.
If you want to learn to shoot in the field, start on a skeet field, but once you start breaking 12 - 15, or so, birds out of 25, switch to sporting clays if you want to learn how to shoot well in the field or marsh.
I guess no one really answered the question about the differences in course layout, specifically.
Trap is shot with the trap in a fixed position in front of the shooters. The shooters fire five shots from each of five positions, which is laid out is sort of a "fan" behind the trap. The trap cycles so that the birds can come out flying on an angle to the left, straight, or to the right, or any place in between. The height of the targets above the ground is fixed, rising then dropping toward the ground as the target flys.
Skeet is also shot from a "fan" layout, but with two traps, one on each end of the "fan". The birds come out of each trap on a fixed flight path. The first trap is the "high house" which throws a target from a height above you at the first station, while the low house throws a bird from across the field flying toward and slightly to the left of you. The birds flight paths are supposed to cross in the center of the field. If you are quick, your longest shot should be somewhere around 21 yards. Shooters rotate around the "fan" to put the targets at different angles and distances, with the last station in the front, center of the fan to take one bird from the high house and one from the low house.
Sporting clays is shot much like an archery field course, where traps are set up, often along the edge or in the middle of a woods and shooters move from shooting station to shooting station. Normally, shooters will shoot 4 to 6 shots at each station. The birds may be thrown as singles, true pairs (two birds thrown at same time), following pairs (two birds thrown from same trap, one quickly after the other), or report pairs (second bird thrown when the first bird is shot at). The courses are usually set up differently every month, to give new types of targets, angles, speeds, etc.
There are several types of targets used on sporting clays courses. The most common is the standard 108mm clay target, but they also have a 90mm and a 60mm target, which are usually faster, harder to see and to hit. Then they have the "rabbit" target which rolls and jumps across the surface of the ground and a battue, which is a disk which is thrown like a standard 108mm target, but being thin, is hard to see. But, as it flies, it turns, showing more of itself and heads for the ground, giving you a quick shot at a rapidly descending target.
The variety of targets and target presentations makes shooting sporting clays more interesting than the other two clay target games.