A Guide to Technology

Dual Core is technology while core 2 duo and Pentium D are the brand name of intel . Dual core referring to any processor package with two physical CPUs in one
Its mean Core 2 duo and Pentium D both are Dual Core processor
Pentium D are first generation dual core processor and  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 Simple facts are,

All Core 2 Duo Processors are Dual Core Processors..
All Pentium D Processors are Dual Core Processors..