How is breathing respiration different from cellular respiration?

Both breathing and respiration are required for all living organisms. Generally, breathing and respiration are often considered the same. However, there is a great difference between these two words.
Breathing is a constant process where you breathe in and out constantly through out the day. It is a process of taking in oxygen and expelling carbon dioxide.

It is all linked. The above answer is correct, but the oxygen taken in your lungs in respiration is used as the electron acceptor in cellular respiration, and the CO2 release in respiration is the final carbon product from the degradation of sugar to to create reducing power (NADH), and to transfer those electrons through a series of cytochromes to create energy (ATP) by pumping hydrogen ions across a cellular membrane until the electrons are finally deposited onto oxygen, creating water. It is essentially the same, just on different levels of magnitude.