It is known that diffusion is one of the most important processes on the cell membrane. It is a spontaneous process, but the rate of diffusion on the cell membrane for different substances can be different. The molecules move from the area of high concentrated substance to less concentrated one. Passive diffusion makes it possible to move substances through the cell membrane. It is called passive transport.
Facilitated diffusion on the cell membrane is a so called passive transport which makes it possible for the substances to cross cell membrane, but with the help of special transport proteins which are used in this process in order to help the molecules to defuse across the cell membrane. However, some large molecules, such as the molecules of glucose, chloride and sodium ions cannot pass through membranes. They need the help of special carrier proteins. Both passive diffusion and facilitated diffusion are related to passive transport because these processes do not require chemical energy.
Active transport stands for the movement of substances from low concentration to high concentration area. This process which occurs in the cells uses chemical energy in order to transport molecules across cell membranes, for example ATP (adenosine triphosphate). It is known as the primary active transport. The secondary active transport uses another type of energy, such as electrochemical gradient. The examples of active transport are the following ones: the uptake of mineral ions into the cells of plants, or the uptake of glucose in the intestines and other ones. (Singer & Nocolson, 1982, p.730)
Singer, S. J. & Nicolson, G.L. (1982). The Fluid Mosaic Model of the Structure of Cell Membranes. Science Press.