Dual Core, Core 2 Duo, and the Core i3 are all dual-core CPUs. The i3 supports hyper-threading though. The Core i5 is a quad-core CPU. And I don't know what the Core i6 is. Maybe you live in the future.
The main difference between the three dual-cores is IPC (instructions per clock cycle). You can't directly compare CPU speed. A CPU may run at 2.00 GHz and another at 3.4 GHz, but the former may have 10 IPC and the other may have 5 IPC. So the former performs faster at lower clock speed than the latter.