They both do the same job. And on an older mouse it's easy to see the similarities. An older computer mouse would have a ball underneath. Then as you moved the mouse around the ball would roll and the computer would count the rotations. A track ball was basically a mouse turned upside down. Instead of moving the mouse to rotate the ball, you'd move the ball directly with your fingers instead.
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They differ in what part is being moved. With a mouse, you move the entire thing. With a trackball, the device itself sits still and you only rotate the ball.
A optical mouse uses a laser to guide your cursor, but a ball mouse has a sphere that touches the surface, as it moves, so does your cursor.
Hope it helped!
The main difference between a mouse and a tough pad is that on a tough pad you have to drag u fingers but a mouse whole mouse is motioning where button are used to select and draggy.