The second type is the gill, a respiratory surface folded out from the body. Gills are chracteristic of many aquatic animals, include fish, aquatic insects, and mollusks. The third type is a system of tracheal tubes that delivers air directly to the tissues. This specialized system works well for small animals, and is found in insects, millipedes, and centipedes. The fourth type is called the lung.
Diffusion moves oxygen across respiratory surfaces.
Diffusion also moves oxygen from the blood to the cells that need it. Again, this could meet the oxygen needs of the cells of small or very inactive animals, but most animals meet their cellular oxygen needs by adding a circulatory system and respiratory pigments, such as hemoglobin. I can't emphasize enough the slow nature of diffusion relative to the fast pace of animal life. Respiratory pigments, generally speaking, are proteins that contain iron or copper atoms, which confer the ability to bind oxygen reversibly. Hemoglobins are a major class of respiratory pigements found in vertebrates and in many invertebrates.