All respiratory systems of animals exhibit the following characteristics:
1. Large surface area
2. A moist, selectively permeable membrane
3. Ability to keep the differences in the oxygen and carbon dioxide concentrations on either side of the membrane to allow diffusion

Here is the comparison between the gills and the lungs:

A. Gills

The gills, which are mainly found in aquatic organisms, are the feathery respiratory structures that allow the exchange of gases that occur underwater. This organ is made up of tiny capillaries that take the oxygen out of the water and release carbon dioxide back to the water.

B. Lungs

Lungs are the respiratory structures of terrestrial organisms. This internal organ allows them to exchange gases between the air and the blood. First, the oxygen is inhaled and it is transported into the lungs. Then, the oxygen is carried through the bloodstream in order to transport the oxygen to the rest of the cells in the body. In turn, the cells exchange oxygen for carbon dioxide. Then, the carbon dioxide goes back into the lungs and gets rid of it by exhaling or breathing out.

Invertebrates that live on land use their skin, mantle cavities, book lungs, or tracheal tubes as the respiratory structures that help them breathe.

On the other hand, vertebrates use their lungs as their respiratory organ, which allows them to exchange gases between the air and the blood.

Whales are aquatic mammals that use lungs for breathing. In this case, they are actually holding their breath underwater. Once they run out of oxygen, they come out to the surface of the ocean to breathe.

The mouth is useful in the process of breathing because it helps in pulling the water in and pumps it into the gills. Once the water passes through the gill filaments, oxygen is taken and moved into the bloodstream of the fish.

The lungs of the birds are quite small and it has nine air sacs. Once the fresh air is inhaled, it moves in a unidirectional flow; hence, more oxygen is diffused in the blood and no old or stale air is trapped in the lungs.

On the other hand, the respiratory system of mammals is made up of two lungs that are located on either side of the heart, which is near the backbone. The airflow in mammalian lungs moves in a bi-directional flow, wherein the air moves into and out of the lungs; hence, the fresh air that comes in is mixed with the old air that has been inside the lungs.