Dual core is just a generic term to mean two processors on a chip.

Core 2 Duo means it is the second generation Core chip from Intel, with Duo meaning it is a dual core one. There are Core Duo chips, being the older first gen ones, and also Core 2 Solo and Core Solo chips that are just a single core processor.

Athlon X2 chips are also dual core.

And while I haven't been keeping exact tabs on the mobile market lately, I do remember it being said Intel is generally on top still for higher processing power and lower power usage.