If you are asking the difference between core2duo and pentium dual core then the c2d was a line of performance CPU's produced buy Intel that has now been dropped with I5 and I7 CPU's on newer platforms. Pentium dual core was the budget CPU's and the name carried on into newer generations. Two compare the two we would have to know exactly which CPU's you are talking about.
a dual core process is just a processor with two cores that work independently so that multiple programs can work at the same time - this is like a V8 engine
a core 2 duo was intels 2nd generation of processors with 2 cores (4, 6 and 8 are now available) - its a brand name like ford, which happens to have a v8 engine