Both types of diffusion involve substances moving across a membrane and going down a concentration gradient. This means that both types of diffusion do not require an input of energy. In other words a substance will move from an area of high concentration to an area of low concentration. Simple diffusion happens when substances move across a membrane without any help. In facilitated diffusion no movement will occur unless the substance has the help of a certain carrier protein which is embedded in the cell membrane. The protein recognizes the particular substance and allows it to pass through the membrane. The protein does its job by actually changing shape. Check out this great animation in the link below.