ual core processors are processors of any brand and model type that have two logical cores within the processor itself, as though it's two processors in one. Examples would be AMD X2's or Intel Pentium D's. Core Duo is a specific model series of processors made by Intel. There is now a release of "Core 2 Duo" series by Intel which is a dual core version series of Core Duo, get it? Any dual core is better than regular Core Duo. Mostly only laptops really use Core Duo. There are a few desktops that use Core Duo, but it's not a very strong processor. The Core 2 Duo is an awesome processor and is blowing a lot of things out of the water. I'm even saying that as an AMD fanboy. It all really comes down to what you intend its use for to determine which is actually better though.
perhaps you are referring to the pentium duel core vs the core 2 duo. in which case there is a huge performance/watt gain!
The pentium D is essentially 2 pentium4 processors slapped together. ok, perhaps it is a little more eligant than that, but you get the general idea. they are hot, they are slow, and they are old, but they were the first mainstream duel core processors offered by Intel.
The core2duo line was a whole new archatecture where they finally ditched netburst archatecture, and went back to something more similar to a pentium3 design. they run cooler, get a lot more performance per clock and per watt, and they were designed to be duel core processors from the start, so the system resources were better shared between the 2 cores. The early Core2Duo processors started out in the 1.5GHz range, but could still keep up with some of the fastest pentiumD and pentium duel core processors. Later gen core2duos are still great processors in spite of their age, and if you are not a gamer I would suggest that you would not see much difference between a C2D vs even some of the newest i3 processors for things like web browsing, email, and office based applicaitons. To really get the most out of one I would highly suggest pairing it with an SSD instead of a HDD.
If you are a gamer, I would suggest a minimum of a core2quad, or an i5 if you could afford one. also, wiki has great info on the intel lineup