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I am confused by the difference between "Cores" and "Processors". A lot of the computers are 2-cores, 4-cores. Does this mean that they have one processor, but with 2 or 4 cores on that single processor?

Also, for intel core i5, it seems that there are 4 CPUs in the task manager, are they referring to 4 core on a processors, or 4 processors with one core each, or 2 cores on 2 processors?

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seems you are not that confused at all. – akira Jul 28 '10 at 13:31
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Yes, a multi-core processor is a single piece of hardware ("one processor") that provides several cores than can work concurrently.

The i5 is a single processor that provides either 2 or 4 physical cores depending on model (see here).

Note that some Intel processors (the i5 included) use hyperthreading, a system where a single processor has (for example) 2 pyhsical cores, but will provide 4 logical cores - allowing the operating system to treat the processor as having more cores than it really does.

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I see, is there any computers that sell multiple processors, multiple-core-on-processor technology? – Graviton Jul 28 '10 at 13:55
@Ngu I think multiple seperate processors (with or without multi cores each) are mainly limited to the Server / Data Centre / Cluster type markets. Don't have a citation for that at the moment though, I'll try and find one.. – DMA57361♦ Jul 28 '10 at 14:01
There are computers that have multiple physical processors, each with multiple cores. Your Task Manager will show the total number of cores (calling them processors, since a core is just a processor that shares the same physical package with other cores). – Marius Gedminas Jul 28 '10 at 14:05
Multiple processors used to be more common in desktops. Nowadays just having more cores has pretty much replaced that need (other than rare circumstances). – Brian Knoblauch Jul 28 '10 at 14:51
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Yes, a "core" is just a processor that's placed on to the same integrated circuit with other processors. See the Wikipedia article for further info on multi-core processors.

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