A gaming mouse can connect to your computer through USB. You can connect it to either a desktop or a laptop. A gaming trackball is similar to a mouse except that it uses a ball instead of a scroll wheel.
Both can be used for controlling movement in videogames. Some mice have extra buttons that can be used for special functions. You might press the button for a crosshair to be activated. Trackballs typically don't include any other buttons.
Gaming mice can work with both left-handed as well as right-handed people. However, they are best suited for righthanders.
Because of their lack of precision, trackballs are not recommended for right-handed people.