Both of them are referring to the same type of processor. Dual Core means processor which is internally divided in to 2 cores. Core 2 is the first generation of the core processor where as Core 2 duo is the second generation of Dual core processor. Code 2 duo will have some advantage like overheating and some other changes are improved in core 2 duo. The main Difference between them is the speed of the processor.
The Latest processor from Intel is i3, i5 and i7.