Simple diffusion and facilitated diffusion both allow molecules to cross the cell membrane without any expenditure of energy by the cell. They are each classified as a type of passive transport.
Simple diffusion is the movement of molecules across the cell membrane from an area of high concentration to an area of low concentration. These molecules have the right size and composition to squeeze through the components of the cell membrane. Substances that diffuse across the membrane do so until the concentrations are equal.
Facilitated diffusion moves molecules across the cell membrane from areas of high concentration to areas of low concentration with the help of protein carriers. These protein carriers act to allow molecules through the membrane that are too large or that have the wrong composition to move through by simple diffusion.
The movement of molecules from areas of low concentration to areas of high concentration requires the cell to expend energy. This form of movement is called active transport. Receptors bind to molecules in active transport, helping these molecules cross the barrier of the cell membrane against the concentration gradient. The process of binding the molecules to the receptors is the action that requires the cell to expend energy.