Not sure what you're asking...
Core 2 duo CPUs are a specific lineup of dual core processors
"dual core" could describe a vast range of CPUs... everything from the old Pentium D series to modern Core i3 Sandy Bridge processors.
There are also "dual-core" marketed CPUs based on "core 2 duo", but those are low-performance parts (think Celerons)
In other words, "dual-core" is a description (2 cores, can be used for all CPUs, wether Intel or AMD), while "core 2 duo" is a name (product name, used only by Intel).
All Core2duos are dual-core, but not all dual-cores are core2duo.