There is a big difference between external and internal respiration. External respiration is basically the transfer of gas between respiratory organs such as lungs and the outer environment. It takes place prior to internal respiration. Internal respiration is the transfer of gas between the blood and cells.
External respiration also known as breathing refers to a process of inhaling oxygen from the air into the lungs and expelling carbon dioxide from the lungs to the air. Exchange of gases both in and out of the blood occurs simultaneously. External respiration is a physical process during which oxygen is taken up by capillaries of lung alveoli and carbon dioxide is released from blood.
Internal respiration or tissue respiration/cellular respiration refers to a metabolic process in which oxygen is released to tissues or living cells and carbon dioxide is absorbed by the blood. Once inside the cell the oxygen is used for producing energy in the form of ATP or adenosine triphosphate.
Here is a video that clearly explains internal and external respiration: