This is what i understand about the whole situation. There are several architectures for CPU's these days. With the x86 processors of old, they ran with a single chip, single "core", and at a 16bit processing depth. The pentium chip introduced the 32bit processing depth.
From here things get hazy. I think it was macintosh that started producing mutiple CPU motherboards with their G3 processor. They did this to compete with intel. Since they couldnt keep up with the evergrowing clock speeds of the intel pentium chips, which where nearing and surpassing the 1GHz mark, they crammed two 500MHz G3 chips on a board effectively increasing clock spead to just under 1 GHz.
Dual and even quad CPU boards have been around longer but were for the most part only for huge mainframe computers and servers. Mac made it available to "the average person"
Instead of following this cue from mac, intel continued with producing the pentium 4 and pushing it to the limits.
AMD was the first to produce a 64bit processing depth chip. The chip did not necessarily have an incredible clock speed (around the 2GHz mark) but could handle much more data. If a 32bit chip was a two lane highway this was a 4 lane.
In order to keep up business with the single core 64bit chip from AMD, they produced the dual core systems. Effectively this is exactly what Mac did way back when, except packaged in one unit. Each core is its own independent processor. Basically two chips smashed and melded together in one. If you look at the specs of these chips you will notice they too have 2GHz clock speeds which seem minute in comparison with the Pentium 4 which has reached 4 GHz in some cases. The distinct advantage the dual core has is the fact that it can handle a 64bit processing depth.
what does this all mean. Well for the most part not much for hte average user. The differences will be seen in large data processing and image renditions.
A dual core or any other 64bit chip will see great advantage in any machine. It will allow the use of 64bit software but if running a 32 bit system, it will be like opening flood gates for the information.
Think of it all like running Win 3.1 (a 16bit application) on a modern computer. It runs extremely fast. Thats because a 32bit chip has twice the capablility of the older 16bit chips
The same works for 32 bit vs 64 bit systems.