A tower is the most common, and is taller than it is wide. The desktop is fla, designed to sit on the desk. A tower is designed to sit on the floor. A tower case can hold many more drives than the desktop case. The desktop, though, is better for placement on the desk, as it allows you to put the monitor on top of it to save space.
Towers come in three main sizes.
The full-tower is the big one, standing two or three feet high. It can hold many drives and usually comes with a larger power supply to run them all. TIt is very expandable and roomy, which allows for excellent cooling. The mini-tower is the most popular. It stands 1.5-2 feet high, and is roomier than the desktop.