In both fish and mammals, respiration requires oxygenated blood to be pumped around the body through the circulatory system, powered by the heart, which draws in deoxygenated blood to add the necessary oxygen, then pumps the result to the rest of the body.
The process, for a fish, involves deoxygenated blood travelling through veins to the heart and entering the single atrium through the sinus venosus (a cavity which exists in the human heart, but is only significant in the embryonic stages). The blood is then forced into the ventricle (again, singular), from which it is pumped out into the large tube known as the bulbus arteriosus, which connects to the aorta. The aorta then carries the blood to the gills where it is replenished with oxygen and relieved of waste gases.
The newly oxygenated blood is then distributed to the body cells via the fish’ arteries, before veins carry the now depleted blood back to the heart.
The mammalian circulatory system is similar in that both involve blood passing through the heart by muscular contraction of each section to force it through the relevant valve into the next, followed by oxygenation in their respective animals’ points of gas exchange. Where the two systems differ is in the time between blood receiving oxygen at the gills/lungs and it delivering the oxygen to the respiring body cells.
In the single circulatory system of a fish, the oxygenated blood travels directly from the gills to the body. Mammals, however, have a double circulatory system, meaning that blood is returned to the heart before distribution. After blood has departed from the right ventricle and received oxygen at the lungs, it is pumped into the separate left atrium of the heart via the pulmonary vein and then it is forced into the left ventricle, which pumps it around the body to arrive at the right atrium again. The reason for the difference is that fish can exchange gas from many points on their bodies, thanks to gills, whereas mammals’ lungs provide only one point of exchange, so a more efficient setup is needed to keep the system working effectively.