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.

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 that 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!