What is exact difference between 1GHz dual core processor and 1GHz single core processor? And what is difference between 2GHz single core and 1GHz dual core processor?
No...the processors are paralleled I believe (as opposed to cascading).
They both operate at 1GHz, but each one shares the processing load. The theory is that two paralleled 1GHz processors process a given amount of data within the same time frame as it would take a single 2GHz processor to process the same amount of data. But they're both still running at 1GHz.
The first article google finds (Yahoo answers) says that a 1Ghz dual core equals roughly 1.6Ghz single core. This debends on many things.. the operating system, how well the software is written, what the software does etc.