Core2Duo is a series in the Intel Core2 family. The 'Duo' is the dual(2) core series of Core2. (Just like how in Core2Quad the 'Quad' is the quad(4) core version of the Core2d series)
Dual core means that the CPU has 2 physical cores. Think of it like having 2 processors in 1.
So as you can see the difference between the 2 is that on is a title and one is an attribute. Core2Duo is in fact a dual core itself.
Hope this helps.