Pull-up

A pull-up begins in a hanging position from a bar or rings with the elbows completely straight and locked out. The movement ends when your chin is at least above the bar without reaching your neck up. Noscrolls has the following pull-up variations:

Strict
A pull-up with no horizontal movement.
Kipping

Most generally this refers to any technique that brings more muscle groups into the movement to aid in completing the movement. Kipping allows the athlete to complete more pull-ups in less time.

Kipping is functional. If you need to pull yourself up over something, life doesn’t care whether you do it strict or with a kip.
Chest-to-bar (CTB)
The chest at some point below the clavicle must touch the bar on every rep. CTB pull-ups can be either strict or kipping.
L
A pull-up done with the legs held straight in a horizontal position as in an L-sit. It’s generally difficult to kip in an L pull-up.
Jumping

Jumping pull-ups are typically used as a way to scale a workout for someone who either can’t do kipping or strict pull-ups, or wouldn’t be able to finish the workout in a reasonable amount of time. The jumping pull-up is just what it sounds like, a pull-up helped by jumping off the ground. The disadvantage to jumping pull-ups is that the amount of scaling they provide is hard to quantify more concretely than the subjective personal assessment of how much force the legs are generating.

Some workouts have jumping pull-ups specifically prescribed. This is usually done on workouts designed to tax cardiorespiratory endurance and minimize the chance of muscle failure.
Assisted

This refers to any other kind of assistance such as a gravitron machine, stretch bands, inclined pull-ups, etc.

The default pull-up for CrossFit is the kipping pull-up. If there is no type specified, kipping pull-ups are always acceptable for an RXd workout.

Greg Glassman describes why we do kipping pull-ups

Adrian Bozman teaches the kipping pullup