Final answer:
The circuit in the circulatory system that moves blood through the lungs is termed pulmonary circulation, which is part of the double circulation system present in tetrapods. This system is more efficient in mammals and birds due to their four-chambered hearts.
Step-by-step explanation:
The circuit within the circulatory system that pushes blood through the lungs is called pulmonary circulation. This system also includes pulmocutaneous circulation in amphibians, where gas exchange occurs through the skin. In contrast, the circuit that delivers blood to the rest of the body, including the brain, is known as systemic circulation. Tetrapods such as amphibians, reptiles, birds, and mammals have a double circulation system, meaning they have separate pulmonary and systemic circuits. The efficiency of this system varies among the classes, with mammals and birds having the most efficient system due to their four-chambered hearts which completely separate oxygenated and deoxygenated blood.