The process of respiration can be divided into the cellular view to the general (cellular respiration to external respiration). Going from the cellular till the external we have:
1- Cellular respiration
Is the aerobic process by which living cells break down glucose molecules to form energy in the from of ATP, that can be divided in three stages, these are: glycolisis (break of glucose into pyruvate), Citric Acid Cycle (Krebs Cycle), and electron transport chain. In this respiration the cell machinery is responsible for from glucose and oxygen form water and carbon dioxide. All the process is intracellular.
2- Internal respiration
The internal respiration is the process of the exchange of gases between the cells and the tissues (internal environment of the body) by the blood vessels and the circulation od red blood cells that carry these gases (oxygen and carbon dioxide). The path of this process is: nose/mouth, pharynx, larynx, and trachea will have the cells oxigenated, the trachea branches and the bronchi will lead to the lungs when the gases exchanges in the tissue will happen. The red blood cells will do the local capture of the gases and the circulatory system will make those cells go to all the tissues in the body.
3- External respiration
The external respiration is the exchange of gases with the external environment. That process occurs in the lungs where the oxygen diffuses into the blood and carbon dioxide into the alveolar air. The internal and external respiration work together in the overall respiratory process, but one happen in the tissues and the other between external environments.
4- How they work together?
The three process are essential for breathing, that's because they work into different levels of tissue and systemic organization. The cellular is the one in the cells that provide the biochemical reactions necessary to the synthesis and conversion of molecules, being the metabolic basis for the respiration to take place, the internal respiration is responsible to distribute the gases into the tissues to make the cellular step possible, while the external respiration makes possible the exchange outside the tissues levels and makes possible to balance the distribution and concentration of the gases in the body.