The common confusion here is that two very different things have the same name. $ce O$ is a free oxygen atom and $ceO2$ is two oxygen atoms chemically bound to form an oxygen molecule.
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There is no common analogy for $ce C$, but $ceN2$ is called nitrogen, $ceH2$ is hydrogen and $ceCl2$ is chlorine, each having the same name as that of their constituent elements.
So, to reiterate, the difference between oxygen $left(ce O ight)$ and oxygen $left(ceO2 ight)$ 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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edited Jan 10 "17 at 2:02
answered Jan 9 "17 at 19:51
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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.
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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.