Asus nexus 7 (2012) and Cyanogenmod
There isn't an Asus one and a Google one: both the Nexus 7 models are Asus-Google collaborations. All Nexus devices are design collaborations between Google and another device manufacturer (Asus, Samsung, or LG).

That said, the two models are completely different, with different SoCs, screens, and cameras. The original Nexus 7 (aka nakasi) has a slightly-over-720p screen, powered by a Tegra 3, and only one camera. The 2013 model (aka razor) has a 1920x1200 screen, two cameras, and a Snapdragon SoC. ROMs are not compatible between the two.