My question are what is the difference between the three phase motor to single phase motor operation and function to the electrical system operation.

Three-phase electric power - Wikipedia, the free encyclopedia

3 phase motor is operating on 380v 3 line voltag (l1,l2,l3... and neutral)and having three phase supply to it.
And the single phase motor operates on 230v line and neutral.

The three phase induction motor or squirrel cage motor is basically the same in construction to the single phase.

The big difference is the three phases gives a 'rotating' field in the windings and so the rotot is able to begin and maintain following the field.

BUT in the single phasem the field simply changes from + to - , basically just going 'bang - bang - bang' which does not allow the rotor to have any direction.

To solve this a number of things are used.

A second winding is wired into the stator and the current in the second winding is made to go a little out of step with the original winding.

This simulates a rotationg field that the rotor is able to react with and then follow, thus begin to rotate.

Some motors are designed so after the motor starts, the starting winding is takes out of the circuit by a centrifugal switch, others are designed so the strt winding is able to remain is service providing a more smoothing run than a single phase winding. (even while running, the 'bang bang' of the fields changing polarity makes it run rough)

Most motors with a low load like your exhaust fans only have one winding but have a small copper ring one one corner of the field poles, this crates a small amount of change of flux on one sode of the pole so it helps to simulate a rotating field.

The torque produced is not very strong, hence the low loads you will find them on and the reaction of the shaded ring has little effect when the motor is running.

Hope it helps

Let me know if it was not what you were looking for or if you need more info