It really is more like two processors in one chip. Don't worry about the insistence you'll sometimes see that "processor" and "core" are somehow fundamentally different things, it's mostly packaging and marketing hooha, not so useful for getting a general idea of how much oomph a system has.
No...
It's like two independent 2 ghz processors, each capable of doing a seperate task while working at their maximum speed (of 2 ghz each).
If you had one 2 ghz processor with hyperthreading, you could do multiple things at once, but the tasks would share the 2 ghz speed.