2 cores without hyperthreading. 4 virtual cores with. but still only 2 actual real cores as they can split threaded workload (progrom instructions) to run 2 instructions at the same time giving the illusion of another core.
in task manager a core 2 duo with hyperthreading will show up as 4 cores turn it off in bios and you will be back to 2.
"Dual Core" is a generic term for any processor that has two cores inside it. AMD and Intel both have dual core CPUs. Even some SmartPhones have dual core processors in them like the nVidia dual core Tegra 250.