What is difference in structure of button start engine and kick start engine?

In a kick start engine, the kicker is connected to a shaft which connects to the flywheel of the engine. As you kick, the linear motion is converted to rotary motion of the shaft which is transferred to the flywheel. When the flywheel makes the required number of revolutions (depending upon whether it is a 2 stroke or 4 stroke engine, though mostly 2 stroke), the power stroke of the engine is reached and the further rotations of the flywheel are continued using the power from the first power stroke which was created manually.

In a button start engine, a self motor which runs on DC voltage is connected to the flywheel. When the button is used, electrical contacts in the self motor touch and it starts. As it rotates, the flywheel connected to it also rotates taking the engine to the power stroke. When the engine starts running on its own, the self motor gets automatically detached from the flywheel and becomes inactive. This mechanism is made possible using a special shaft. As the motor turns clockwise (caused by the electric supply given using the button), the motor moves towards the flywheel such that the motor's shaft comes in contact with the flywheel and rotates it. When the push of the button is released, the self motor stops and the flywheel's independent rotations cause the self motor to move back on the shaft thus detaching itself once the engine starts.