Different Types of wheel combinations are used for building Mobile Robots to providing Different degrees of freedom, Support, etc..

These are normal circular wheels of a particular wheel base and diameter.
These wheels are capable to roll only on its periphery. Lateral roll is not possible.
while rolling slippage over the periphery is zero.
Manufacturing cost is very less because of its simple geometry.

wheels having rollers over the periphery with its axis at an angle of 90 degrees to the base wheel axis.
Roll in two directions is possible, one along the base wheel periphery and second along the rollers.
Slippage is there when these wheels are in motion.
These wheels work on slippage.
Manufacturing of these wheels is an expensive affair.
Typically 3 or more wheels are mounted over the chassis for multi directional motion.
The orientation of mounting of these wheels is in the form of a polygon.

3WD_Omni_Wheel
3WD Omni Wheel With PWM

These are wheels quiet similar to Omni but the rollers are inclined at an angle of 45 degrees with respect to the axis of the base wheel.
Depending on the position of the wheel the rollers are inclined by 45 degrees either to the left direction or right direction.

4WD_Omni_Wheel
4WD Mecanum Wheel With PWM