dual core means having 2 core, core 2 duo is one series of processor that are dual core, there are others such as current i3, and i5 mobile that are also dual core.
Summary:
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