Let me put forth the difference between Dual core and core 2 duo processors in very simple words
Dual Core – has 2 cores in a single silicon chip
Core 2 Duo – is the name given by Intel to its second batch of dual core processors
So core 2 duo is a type of Dual core processor.
processors that have 2 cores in them are collectively called as dual core processors regardless of which manufacturer it came from, while those that have 4 processors in a single chip are called quad core and those that have 8 processors in a single chip are called dual quad core or octa core.
Putting all the above together
1. Dual core is the generic name given to processors that have 2 cores on the same chip
2. Core 2 Duo is the second line of dual core processors from Intel
3. Other dual core processors aside from Core 2 Duo are the Core Duo from Intel and the X2 series from AMD
4. All Core 2 Duo processors are dual core but not all dual core processors are Core 2 Duo