C + O2 is equal to C + O, how is that possible
When thinking about chemical reactions it is very important to know which chemicals may react with each other. Jun-Goo Kwak already pointed out the nature of oxygen.

A quick reminder: The ground state of elementary oxygen is the triplet biradical $\ce{o2}$, which is a gas. This is what we have on the surface of the earth. Carbon however comes in many  different forms in nature. The most popular and often is graphite. Other forms include diamond, fullerenes and graphene.
At one point in your life you haw almost certainly come in contact with graphite: coal. As the principle repeating unit is carbon itself, its formula will be written as $\ce{C}$.

As for the binary combination of oxygen and carbon, there are also many different modifications. The most important of them are carbonmonooxide ($\ce{CO}$) and carbondioxide ($\ce{CO2}$). Like Uncle Al stated there are also suboxides known, which are usually byproducts of incomplete combustion (if not targeted explicitly).

Having said all that, if you burn coal, the following main reaction will happen (1):

$$\ce{C + O2 -&gt; CO2}$$

However, given the right conditions (excess carbon) also carbonmonoxide  may be formed (sum of reaction, 2):

$$\ce{2C + O2 -&gt; 2CO}$$

The reaction itself will detour via the Boudouard reaction, which is very important in blast furnace processes. First forming carbondioxide via 2 and then convertin excess carbon to carbonmonoxide via 3:
$$\ce{C + CO2 &lt;=&gt; 2CO}$$