The heart and lungs are joined into each other as if they were one single unit. The same nerves keep the cardiothoracic system working in sync - mainly through the vagus nerve, I think. The biggest blood vessels in the body run between the heart and lungs.
well, when you take oxygen into your lungs it transfers from your lung's bronchial tubes and is sorting into your blood stream which is pumped through your body by your heart so the oxygen can reach all of your body via your blood
The alveoli (part of the respiratory system) transfers oxygen into your blood (part of the circulatory system). Your blood transfers CO2 into your alveoli which gets exhaled. So these organ systems are related because they exchange gases