Dual Core is a general term (not related to any brand) meaning that there are two cores inside a single physical chip. Similarly Quad Core means that there are 4 cores inside a single physical unit.
Core 2 Refers to a Processor Model from Intel like the Pentium, Pentium 2, Pentium 3, Pentium 4 etc. Core 2 Duo means that its a Dual core variant belonging to the Core 2 line of processors. Similarly Core 2 Quad means that its a Quad Core processor belonging to the same Core 2 family.
Core2 is the latest generation of processors from Intel. The earlier one was called Core and came in Core Solo (Single Core) and Core Duo (Dual Core) variants. Earlier to that there was the Pentium D line which were again Dual Core processors from Intel. Similarly AMD also has a Dual Core line called the Athlon X2.
It seems that though Dual Core is a general term, the computer vendors have began to refer to the Pentium D lineup as "the Dual Core". But as I mentioned its a general term.
Hope this cleared up things for you.
Sumeet a.k.a NEO said:
but can u giv me specifically the diff in the speeds??
The clock frequency means nothing and how the frequency is used is what matters. The Core 2 Duo use a completely different architecture from the Pentium D line and hence even at the same frequency the Core2 will be faster than the Pentium D. A Core 2 Duo clocked at 1.86 GHz (E6300) can hold its own against a Pentium D clocked at 3.2~3.4 GHz. These processors are also highly overclockable adding to their value. If you want a Dual Core processor and cannot go for the Core 2 line due to the cost, then it would be better to go for the Athlon X2 rather than Pentium D.