Mechanical pencils, also known as propelling pencils, allow you to extend the lead from the pencil casing as it wears away. When you press the button on top, the lead is pushed out in small increments. It means that you can have a very fine lead which never needs sharpening.
Clutch pencils, also known as lead holders, are slightly different in the fact that they usually have a wider lead and when you press the release button on the top of the pencil, the lead is free to move in and out of the pencil. When you let go of the button, the clutch mechanism holds the lead in place at the desired length. As these leads are wider, they do need sharpening and clutch pencils often come with an inbuilt sharpener.