There are in total, 6 types of wheels that are allowed in VEX. These are usually used for movement of the chassis but there are many other use cases as well. VEX does not limit chassis movement to wheels and you could use any other sort of movement but wheels are usually the most effective as it is fast and reliable. These wheels also come in different sizes such as 2.75", 3.25", 4", and 5". But in most robots, people will use the 4" wheels for chassis movement.
These wheels are the standard ones for chassis movement. They can be used to make flywheels and any other mechanisms as well. They have some traction but when turning with these wheels, it is not as smooth and causes a lot of friction.
These wheels are usually used as "assistance wheels". Due to its small size, it can be used as a tip-proof mechanism where it can be the 5th and 6th wheels of the robot allowing it to have a bigger stance, proofing it from falling. These have the most friction when turning so it is not recommended for using as a motorized wheel, although due to its high traction, it is very rigid.
Omni-wheels are the most common wheels found in most robots. These have the least friction as the little rollers allows the robot to turn freely although one negative is that the rollers could lead to the robot not moving straight when it is commanded to due to the rollers slipping. This can be fixed by using a combination of basic wheels and omni wheels.
These wheels aren't used as often as they are quite similar in function to the basic wheels. Although it advertises traction, it is quite similar to the basic wheels with only little more traction.
The one shown in the photo is the only 5" wheel available and although not commonly used for chassis movement, it is used as a part of a flywheel quite often. The increased surface area allows for the ball to gain more speed as a flywheel. These are not recommended for chassis movement as the extra inch diameter leaves less space for the robot to occupy with no upsides as most games are built with 4" wheels in mind.
Although these wheels look exotic, it is quite useful as it is the only wheel that could be used to move in all 8 directions. It does this by motorizing all 4 motors and using a combination of directions on each wheel to move in a certain direction. A negative point for this wheel is that it is quite slow and does not reach high speeds.
Courtesy of RobotEQ (Link)