Core Duo is Intel's first dual-core CPU. It's a whole new architecture for Microsoft, using two cores on a single die, which, put simply, gives you two chips in one package. Running at lower speeds than the old Pentium line, the Core Duo conserves substantial power vs. ratcheting up clock speed while offering what was, at the time, record-breaking performance.
Now there's Core 2 Duo. In many ways Core 2 is the same as Core: The chips are built using the same production process and fit in the same sockets as Core Duo chips. Putting aside Core 2 Extreme (a fancy version of the Core 2 Duo), you won't see many spec changes: Both chips have the same frontside bus speed of 667MHz, but Core 2 Duo is now available at somewhat faster clock speeds (as I write this, 2.67GHz chips are available). The frontside bus communicates between the CPU and RAM (and other components), and it's a notorious performance bottleneck for computers. The Core 2 also has the same L2 cache that the Core has. However, there are architecture changes to the silicon that give the Core 2 more sophisticated processing abilities. Both chips exist in desktop and laptop versions.
Why does all of this matter? Performance, pure and simple. In my tests, Core 2 Duo computers outperform Core Duo computers on tasks across the board, from rendering graphics and video to spell-checking documents. The speed improvement varies widely, but on average it's about 30 percent. That's significant in an industry that thrives on tiny, incremental improvement. Better yet, there's not an appreciable difference in battery life on notebooks, as power consumption for both chips (at the same clock speed) is about the same.
Now let's consider pricing. Initially, Core 2 chips were more expensive than Core, but that has changed, as Core is practically gone from the desktop market now. Surprisingly, you can now get a 2.13GHz Core 2 CPU for less than the price of a 1.66GHz Core CPU.
Still, expect to see some systems still on the market that use the Core CPU, especially in laptops. Performance is still very good with Core, so don't feel like you're getting second-class goods if you buy a Core Duo notebook, but remember you are buying a chip that Intel is no longer actively selling, and prices for Core 2 systems aren't really any different than they were for Cores. If it was my money, I'd hold out for a Core 2 system unless you got a great deal on a Core... which will be all but vanished from the market in a matter of months