Core
If referring to the name of the processor or the architecture the core of the processor refers to the under-the-hood name of the CPU. As a similar analogy, wheres a processor may liken to "pickup truck" or "car" (or even a specific make and model), the core would like to "V8" or "HEMI" or something as such. To add to the confusion, there are subtimes revisions of cores and often in common computer speak, core names may even be shorted down. A quick list of some cores past present and future:
Intel: Deschutes, Covington, Mendocino, Katmai, Coppermine, Willamette, Northwood A, Northwood B, Northwood C, Banias, Dothan, Gallatin, Prescott, Cedar Mill, Smithfield, Presler, Dempsey, Paxville, Tulsa, Millington, Montecito, DP Montrale, Montrale, Millville, Whitefield, Dimora, Tukwila, Allendale
AMD: Spitfire, Applebred, Morgon, Thunderbird, Palomino, Thoroughbred A, Thoroughbred B, Thorton, Barton, Roma, Georgetown, Albany, Palermo, Newcastle, Winchester, Paris, Venice, San Diego, Clawhammer, Toledo, Denmark, Troy, Egypt
The core name may also be referred to as the codename of the processor. Please note the above is a brief list of examples, not a complete list of all available cores.