Some of the confusion about cores is due to the fact that Intel puts different i# designations on their chips depending if they are "Desktop" or "Mobile" CPUs.
A Desktop i5 is (usually) going to be a Quad Core CPU without Hyperthreading, and a small amount of cache missing (either due to manufacturing defect, or fused off), while a mobile i5 is (usually) going to be a Dual Core CPU with Hyperthreading.
I say usually because Intel keeps messing with their designations from year to year, as new chip generations come and go. After a few years, it gets ... messy
The main differences between Desktop and Mobile chips are in two ares: Power Consumption and built-in GPU.
Desktop chips are going to have smaller integrated GPUs, but a much higher power consumption profile (TDP) - which translates into higher clock speeds. The less powerful graphics are made up by the fact that desktop users are more likely to (and can) have a dedicated graphics card.
Mobile chips need to work in laptops where battery life is very important and tiny systems where cooling is very important. The clocks speeds they give up compared to their desktop counterparts give them a huge edge in power (and heat) - To get that last gigahertz of clock speed takes a disproportionately large amount of the total power consumed, and produces a proportionately large amount of the heat that has t be dealt with.
Mac Minis have always used the laptop chips, allowing for their tiny size and great efficiency.
Anyway, back to the OP: Given the usage situation you described, I suspect that you will want to upgrade to an SSD drive as well as making sure you have enough RAM. For a database application that is going to get some use, the SSD should result in much better perceived and actual performance compared to a regular hard drive. The difference I suspect is going to be *many* times greater than the clock speed differences between a 2011 quad-core server and a 2012 quad-core mini.
