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A dual core is any CPU using 2 cores. Core 2 Duo,i3 and some i5 are dual cored.
Core 2 Duo is a line of dual cored CPU's made by Intel. They are mostly outdated by now.

Core i3 is kind of the successor to Core 2 Duo. They are all dual cored and some are pretty good for their price(i3 2120 for instance).

Core i5 is the middle term so to speak. Some are dual cored others are quad cored. Just read some threads and you will surely notice the use of the 2500k.

Core i7 (there's no i6) is the top end stuff. Powerful and expensive they use 2,4 or 6 cores.

This was a very basic explanation and to put it even easier:
core 2 duo> i3> i5> i7