What's the difference between $W$ and $dW$? They are both work done and have similar formulae (same dimension). But I don't know the difference between them.
$dW$ here ISN'T power.
The difference is that $dW$ is an infinitesimal ''quantity'', whilst $W$ is not. I assume the context here is thermodynamics, which make use of calculus. In calculus there is the concept of the infinitesimal. I suggest, for you, to concern yourself with the structure of calculus if you are to tackle thermodynamics.