It wasn't confusing enough that Intel named their CPU core 'Core' or that they put 'Duo' after it if there wre two 'Core' cores packaged together, but they also put a '2' after it if it was the second generation, then they dropped the generation number from the name in the third generation, making that the first generation of their new numbering scheme of which you're discussing the second generation.
Heh, yeah. In the moment I couldn't come up with the brief, unique descriptor and reached for the modern shorthand.