Logically enough - the Core temps are the temperatures of the individual cores. It's normal for them to be a few degrees different. The CPU temp is the temp at an external sensor (at the heat spreader).
At those settings and with an aftermarket cooler you'd really be expecting those temps to be a bit lower than they are currently.
Check the voltage (VCore) value of your CPU using CPU-Z. Compare this to the nominal value from the Intel website. There's no need to have it towards the upper extremity of the nominal range if you're not overclocking.
Secondly, how did you apply the thermal paste? There are various techniques such as the line method and the 'blob in the middle' method but the basic idea is to have as thin a layer as possible.
How is the general airflow throughout your case? This is a pretty good guide to the basics of case airflow: