I thought my electric car charging unit uses 6.6 kW of power. However, I found the label and it actually says 6.6 kVA. When I saw this I thought something along the lines of...


  Well, $ P=VI $, therefore kVA must be the same thing as kW... strange, I wonder why it's not labelled in kW.


So a quick Google search later, and I found this page, which has a converter that tells me 6.6 kVA is actually just 5.28 kW. The Wikipedia page for watts confirmed what I thought, that a watt is a volt times an ampere.

So what part of all this am I missing, that explains why kVA and kW are not the same?

The problem is that the formula $P=I\ V$ is correct when dealing with DC circuits or with AC circuits where there is no lag between the current and the voltage.  When dealing with realistic AC circuits, the power is given by 
$$
P=I\ V\ \cos(\phi),
$$
where $\phi$ is the phase difference between the current and the voltage.  The unit kVA is a unit of what is called 'apparent power' whereas W is a unit of 'real power'.  Apparent power is the maximum possible power attainable when the current and voltage are in phase and real power is the actual amount of work which can be done with a given circuit.   