The difference between Core 2 Duo and Core Duo (Dual Core)
Dual core is simply a generic term referring to any processor package with two physical CPUs in one.
The Pentium D is simply two Pentium 4 Prescott cpus inefficiently paired together and ran as dual core.
The Core Duo is Intel's first generation dual core processor based upon the Pentium M (a Pentium III-4 hybrid) made mostly for laptops (though a few motherboard manufacturers have released desktop boards supporting the Core Duo CPU), and is much more efficiently than Pentium D.
The Core 2 Duo is Intel's second generation (hence, Core 2) processor made for desktops and laptops designed from the ground up to be fast while not consuming nearly as much power as previous CPUs.
The Pentium D, Core Duo, Core 2 Duo and Athlon X2 are all current CPUs that have dual cores in one package.
Note - Intel has dropped the Pentium name in favor of the Core architecture.