I am a student of 10th grade, and I eagerly want to learn biology. What is the difference between respiration and breathing?
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.
Breathing is a part of respiration but respiration is not a part of breathing.
Breathing is a process through which oxygen is taken into the body for use in respiration. This involves physical movement to take oxygen (into the lungs) and also chemical action (haemoglobin-carries oxygen from lungs to blood and carbon dioxide from blood to lungs).
But respiration is a chemical process that involves the break down of the glucose that was formed during digestion to form energy (chemically, energy is Adenosine Triphosphate) for our everyday or metabolic processes.
An addition to previous answers plus some clarification
The term respiration originally meant breathing i.e inhaling and exhaling (See here). It was believed that it is the oxygen and in turn the act of breathing is what lets an organism survive.
After substantial research it had been found that, in individual cells it is the ATP production by mitochondria that requires oxygen (as a terminal electron acceptor) and therefore for a cell, respiration is basically the electron transport chain (ETC).
Note that glucose or any other food molecule or its breakdown has got nothing to do with respiration. The process of glucose breakdown i.e glycolysis is not a part of respiration. TCA cycle is however considered a part of respiration because it is coupled with the ETC.
Later it had been found out that molecules/ions other than oxygen such as Fe3+, Fumarate etc, can also serve as the terminal electron acceptor. So cellular respiration expanded to include these cases as well; these fall in the subcategory of anaerobic respiration.
Note that fermentation also is a pathway that generates energy in the absence of oxygen but it is not considered respiration. It was previously classified as anaerobic respiration (if I am not wrong) but not any more.
So you can see that respiration which was originally synonymous with breathing now denotes a very specialized process. However, respiration is still used to mean breathing and distribution of oxygen in the body when cellular physiology is not in discussion.