Socket Type Definition

A CPU socket is the location where a CPU is secured on the motherboard. A socket is what allows the processor to communicate with the rest of the computer. Sockets make it very easy to install and remove CPU's. Each CPU generation will require a specific socket type. The motherboard and the processor must use the same socket.

Intel's Socket Types:
LGA 1150 - Used by Haswell CPUs (4th Generation i3, i5 and i7's)
LGA 1155 - Used by Sandy Bridge (2nd Generation i3, i5 and i7's) and Ivy Bridge CPUs (3rd Generation i3, i5 and i7's)
LGA 2011 - Used by high end i7's

AMD's Socket Types:
AM3+ Used by Vishera, Zambezi and other CPU's
FM1 Used by Llano CPU's
FM2 Used by Trinity and Richland CPU's

Architecture or Core Definition

The architecture or core is how the ISA or instruction set architecture is designed in the CPU. Newer architectures greatly help with efficiency and allow for more performance per gigahert. It is important to always buy the latest architecture. Here is a wiki article containing a list of Intel and AMD's architectures.