A whip tends to be faster and much closer to the ground. If a whip is done correctly, you should almost be able to touch your hands to the ground. In essence, it's a high and fast back handspring. Whip backs can be arched to get around fast, but if the floor is bouncy it is usually not needed.
A layout is supposed to be much higher and much more "floaty". They are much more similar to a back tuck than a whip back. Layouts always need to have a nice hollow shape when coming around.
Funny enough, doing a bad layout can result in a whip, while doing a back whip can result in a layout. Really, all it depends on is how you set.
You start the set with your feet more in front of you in a whip. This helps you go lower, but really you get the speed and shape from the "whip" part. You pretty much throw your head back and then snap into a hollow very fast, which helps you gain speed.
With a layout you set straight up and down or with your feet a little behind you. This will send your energy going up instead of out like a whip. Also, you hesitate on the set. Unlike whips where you immediately throw your head back, you set up with your arms much slower and controlled, staying hollow the whole time.
Good luck, and like all skills, it just takes practice!