How can we differentiate between respiration and breathing?
There are two uses of the term respiration: physiological respiration and cellular respiration

Physiological respiration involves the intake of outside oxygen and its distribution to the tissues of the body. Breathing is a part of physiological respiration and functions to bring oxygen into the lungs and expel carbon dioxide. 

Cellular respiration is a chemical process by which energy is obtained within individual cells from biomolecules like glucose. In aerobic respiration, oxygen is used. Cells can also use fermentation and, for some, anaerobic respiration to obtain energy.