What is the difference between O & O2

What is the difference between $\ce{O}$ and $\ce{O2}$.


If C is carbon and then why $\ce{O2}$ is oxygen.




The common confusion here is that two very different things have the same name. $\ce O$ is a free oxygen atom and $\ce{O2}$ is two oxygen atoms chemically bound to form an oxygen molecule.


There is no common analogy for $\ce C$, but $\ce{N2}$ is called nitrogen, $\ce{H2}$ is hydrogen and $\ce{Cl2}$ is chlorine, each having the same name as that of their constituent elements.


So, to reiterate, the difference between oxygen $\left(\ce O\right)$ and oxygen $\left(\ce{O2}\right)$ is that the former is an oxygen atom while the latter consists of two $\ce O$ atoms bound together, forming a molecule also called oxygen.


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Sometimes we use terminology a little loosely.


When we are just talking about the element, then just using the symbol by itself is clear. But sometimes we need to describe how the element appears in the world or in chemical reactions. Then it isn't enough to describe just the element, we need to know something about how it is found under normal conditions. Oxygen is usually found as a diatomic gas (which is why we write O2). Since this is by far the commonest way we find free oxygen in nature we often describe it this way anyway unless there is a reason not to. 


Nitrogen is also mostly found in pure form as a diatomic gas (N2). Carbon, however, is usually found as a solid and never as a simple molecule (diamond and graphite are both covalently bonded solids) sort is rarely useful to describe its normal molecular form as there isn't one. We might talk about sulfur as S or, if we care about the allotrope we might specify S8, though there are others common in the lab.


It matters little which version you use to describe the *element*. But, if you are talking about reactions, it is usually worth describing the molecular form of the element you are talking about. Oxygen isn't always O2 but can be formed (in the upper atmosphere or in some reactions) as O3. 


Chemists mix and match their terminology somewhat freely when it doesn't matter much, but try to be as specific as possible when it does.


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O is a singular oxygen atom. O2 is a molecule made of two oxygen molecules. Our atmosphere is made of mostly O2, which our bodies have evolved to breathe. We breathe in O2 and cellular respiration requires it (C6H12O6+6O2→6CO2+6H2O). 
  
  

O is oxygen, while O2 is dioxygen.
  
  

Examples of other oxygen molecules are: 03 which is ozone (trioxygen), there's O4 that is metastable and is actaully made up of two O2 molecules (tetraoxygen), and O8 which is a form of pressurised solid O2 (when you freeze O2 to below around 55 Kelvin and pressurise to around 10 GPa (1.45e+6 psi)it becomes known as ε oxygen or red oxygen due to the color changing from blue to red).


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Context is important. C is the atomic symbol for carbon and can represent not only the element, (but one or more) atoms of the element, as well as the element as it exists in the understood (implied) conditions. Same is true for O or N or actually any element. However, *elemental* O and N are both commonly found as diatomic molecules O2 and N2. I will turn your question around: since oxygen and nitrogen are commonly represented by their ground state chemical compounds (at STP) why isn't carbon represented by Cgraphite? (and why isn't sulfur represented as S8?). The reason is fairly straightforward: it is because the *actual compound* we have in front of us may be difficult to determine (in the case of C or S), while there's generally no question about O2 or N2 being the compound we have. So, we use the atomic symbol to represent the elemental material when it is either of indeterminate or of variable composition. Carbon, in particular, is often found or used as allotropes different than graphite. So we are as specific as we can be, without risking being wrong. (If we specify O2 then sure, there might be some trace amounts of O3 or even O. around, but we assume those complications are (also) understood.) It is *much* harder to do that with solid elements, so we avoid being too specific (remember, as scientists, we should be able to justify our claims, including the nature of the materials we are discussing) by using the atomic symbol. Liquid bromine, for instance might be represented as either Br(l) or Br2(l) although the second is the ground state elemental form (at STP). {Just to correct one of the answers, N2, and *not* O2, composes over 70% of our atmosphere by volume.}


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Symbol of an element only represent one atom of that element.The chemical formula of an metal element is same as its symbol however this is not true for non metals as they exist as covalent molecules.The chemical formula for an element takes in to consideration of the different stable compositions or naturally occurring forms of that element.This is why hydrogen has the chemical symbol ( $\ce{H}$) and chemical formula as $\ce{H2}$. Terminology is important to understand the difference between element symbol and its stable composition.It is important to note that even though atomic symbols and it's naturally occurring formula are two different things the name used to describe the two things might be same. For example oxygen symbol is $\ce{O}$ and $\ce{O2}$ which is its naturally occurring form is also referred to as oxygen and sometimes oxygen molecule which is the correct way to describe it. 


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