Core 2 Duo is a brand name for a line of intel dual cores, all Core 2 Duos are dual core CPUs but most dual core CPUs are not core 2 Duos.
Quick list of other dual cores: Pentium D, Celeron D, Celeron Dual Core, Pentium Dual Core, Athlon X2, Athlon II X2, Phenom X2 Phenom II X2, i3
Only the Celeron and Pentium Dual cores share architecture with the Core 2 duos the other ones are very different but still dual cores.
Celeron D's were single core Prescott celerons, I know the name is misleading but Intel wanted it to mean "desktop"
I think they did it to confuse consumers into thinking they got a dual core, seeing as their Pentium D chips were dual core.