What is the difference between PGA and LGA

Multiple processors let your computer do literally two things at once (instead of only seemingly doing two things at once, but actually just swapping between tasks extremely rapidly).

Multiple cores are the same. The advantage of multiple cores over multiple processors is that they share some bits of the CPU, e.g. the second level cache, which makes it possible for them to work even more efficiently if they have some shared data. This makes them much cheaper to manufacture. A single dual-core CPU also takes up less room than two single-core CPUs, which is an important factor these days with everyone moving to laptops.

There may be some performance differences, but nothing you're likely to notice.

http://en.wikipedia.org/wiki/Pentium_Dual-Core

The Intel Dual Core is its own product line of Intel processors.

http://en.wikipedia.org/wiki/Intel_Core_2

The Intel Core 2 is also another product line of Intel processors.

The pentium dual-core processor is a one of Intel's value or basic processors available. That is why you save so much going with that processor. The Core 2 is the more powerful desktop processor from Intel, hence why you pay more for it.

Here is a review comparing performance between the two: (This is well put together)

http://expertester.wordpress.com/2008/05/30/core-2-duo-vs-pentium-dual-core/

And a forum discussion about the differences:

http://www.devhardware.com/forums/intel-processors-30/pentium-dual-core-vs-core-2-duo-188459.html

I assume you mean the difference like on this inspiron 537 between the two middle models:

http://www.dell.com/content/products/productdetails.aspx/desktop-inspiron_537s?c=us&cs=19&l=en&s=dhs

If you notice next to the processor names is the intel e5200 and the intel e7500. These are the processor numbers you can look up on the internet for futher specifications and reviews.

The E5200 is listed under the Pentium Processor for Desktop on intel's website:

http://processorfinder.intel.com/List.aspx?ParentRadio=All&ProcFam=2841&SearchKey=

The E7500 is listed under the Core 2 Duo Desktop Processor

http://processorfinder.intel.com/List.aspx?ParentRadio=All&ProcFam=2558&SearchKey=E7500