Dual core is the general term for processors with two independent CPUs. Core 2 Duo is Intel's brand name for one of their dual core processors. It's akin to the difference between a compact car and a Honda Civic.
Actually The Core 2 Duo processor has two parallel cores inside a single physical package and the two cores sharing their load. so, the core 2 duo processor is faster. But in dual core processor the two cores in Series and the both cores are working at same time. So it is much slower then core 2 duo processor. And also the multi-tusking performance also less in the dual core processor.