What is the difference between "Intel Pentium Dual-Core" and "Intel Core 2"

A Pentium Dual Core is essentially two cores based on an older design slapped on the one chip. They have a reputation for getting rather warm under load.

Core 2 Duos are based on a newer core design that is significantly quicker clock-for-clock in most operations than a Pentium Dual Core, and consumes less power (so giving off less heat) while doing so. They also tend to come with much more on-die cache, helping speed even more in many cases. Also, the "Core 2" core design was build with multi-core in mind so is more efficient in terms of how its cores interact (i.e. when sharing on-die cache and such) than the Pentium Dual Core (which was designed initially to be used as single-chip single core or multiple single-core chips).

So a C2D will operate faster, even at lower clock speeds, while using less power.

There are single-core Core 2 based designs, which may complicate the comparison a little more. If you are looking for dual core make sure you get one marked "duo".

Not all Core 2 chips support VT, which may be a consideration if you plan to use virtualisation a lot (though VT is not required for this, it can being performance benefits depending on the virtualisation solution you chose). See http://en.wikipedia.org/wiki/List_of_Intel_Core_2_microprocessors for more detail (look for those that have VT listed in the features). I believe that no Pentium Dual Core chips support VT as the basic core design predates this feature by quite a time.