What's the difference?
Hop - takes off from one foot and lands on the same foot.
Jump - takes off from two feet.
Leap - takes off from one foot and lands on the other foot.

Cat Leap - jump with one leg straight and the other bent and held forward

Fish Jump (also known as Wolf Jump) - pike jump with one leg straight out in front and the other bent.

Half-in half-out - A back flip with a 1/2 twist into a front flip with a 1/2 twist. Can also be done in tuck, pike, and a strait position.

Hitch Kick - hop with the free leg held straight out and the other leg briefly leaving the mat.

Johnson - switch leap with ¼ turn (on floor). On beam it is often called a switch-¼ or switch-side leap.

Popa - straddle jump with a 1/1 turn.

Punch Brani - Like a punch front except add a 1/2 twist. Can also be done in tuck, pike, and a strait position.

Punch Front - Forward moving flip punching off both feet.

Rudi - A front flip with a 1 1/2 twist in it.

Randy - A front flip with 2 1/2 twist in it.

Ring Leap - jump with head thrown back and knees bent (one to the front and one to the back) and raised towards the head.

Sheep Jump - jump with back arched and both legs bent backwards and raised towards the head.

Shushunova - gymnast jumps up in straddle position, and rotates her body forward to become parallel to the mat or beam. She then falls to lie facedown. Also may done with ½, 1/1 or 1 ½ twists. On floor, this element is often combined with other leaps such as Popas, Johnsons or wolf jumps. On beam, the Shushunova usually takes place facing perpendicular to the beam.

Sissone - leap where the gymnast takes off from two feet and jumps up in split position with the back leg higher than the front.

Split Leap - leap where the gymnast takes off from one foot with one leg horizontally to the front and the other to the back.

Stag Jump - rear leg is straight, front leg is bent. A double stag is done with both legs bent.

Straddle Jump - jump with legs straight out to the side.

Switch Leap - split leap where the front leg moves to the back and the back leg to the front in mid-air.

Tours:
Single Tour - A jazz dance jump where there is a full revolution left or right in the air with the body totally contracted and erect (as if the person represents a standing pencil) and feet are together. 
Double Tour - A jazz dance jump where there are two revolutions left or right in the air with the body totally contracted and erect (as if the person represents a standing pencil) and feet are together. 
In both "tours", the gymnast would start or end frequently in fourth position more than in second position. Both jumps also occur in classical ballet too ... and it would be called "tour de l'air" in French....or "turn of the air", literally.

Wolf Jump (also known as Fish Jump) - pike jump with one leg straight out in front and the other bent sharply back with knees together.

Yang Bo - jump with legs in oversplit and back arched. Yang also invented a switch leap with the same head position. Liu Xuan did beautiful Yang Bo leaps (both regular and switch leap) on beam.

** Note: Many of these are named after a gymnasts on one event but not the other.

This list is incomplete, please contribute more: Email us -- Thanks!