What is the difference between breathing and respiration?

This was a question I was commonly asked when assisting GCSE science students in year 9/10. 

Breathing is simply taking air in through your nose/ mouth and down into lungs (and then breathing it out again). - I would act this out. 

In the air you breathe in, there is about 21% oxygen. This diffuses from the lung into blood and is carried around the body. Respiration is the process of cells using this oxygen to create energy. This is done inside the cell, in little energy factories floating in the cell called mitochondria.