Do respiration and breathing mean the same thing?
I think you mean respiration (?)
Respiration is the movement of oxygen from the outside environment to the cells within tissues, and the transport of carbon dioxide in the opposite direction. So basically the process of inhaling and exhaling air.
A more scientific explanation is: The sum total of the physical and chemical processes in an organism by which oxygen is conveyed to tissues and cells, and the oxidation products, carbon dioxide and water, are given off.
Side fact - The primary organs of the respiratory system are the lungs, which function to take in oxygen and expel carbon dioxide as we breathe. The gas exchange process is performed by the lungs and respiratory system.