What is the difference between a single phase motor and a three phase motor?

Two more phases of electrical power needed to make it work.

They are wired differently and need different power supply.

A single phase induction motor is one designed to run on a single phase supply.
In reality there is some provision for starting, as single phase does not provide
A rotating field, but one that reverses 180 degrees.
Three phase induction motors have three phases, so the first requirement is a three phase supply.
The three phases are 120 degrees apart, so that a proper rotating field is produced.
They tend to be smaller and cheaper and run smoother than an equivalent single phase motor.
They can be more efficient than some single phase motors.
As some of these can be large, they can need a specific starting arrangement to reduce the sudden surge at start-up, and perhaps to control the acceleration.