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Richland is the successor to Trinity, which are AMD's current generation A-series APUs. It will have the same CPU as Trinity, but GCN (Radeon HD 7000 series) graphics. AMD is claiming substantial improvements in graphical performance. Also, Richland is shipping now, so it should be available for purchase soon.
Kaveri is the successor to Richland, and has Steamroller cores. That should be substantially faster on the CPU side. It's a 28 nm chip, as compared to 32 nm for Trinity and Richland, which should allow for a larger transistor budget and better energy efficiency. Kaveri was rumored to be delayed into 2014 or cancelled outright, but AMD is insisting that it will launch late this year.
Kabini is AMD's netbook chip, and Temash is the tablet variant of it. They're the successor to Brazos (E- and C- series) and Hondo (Z-series) respectively. Both use new Jaguar cores, as compared to previous generation Bobcat cores. Kabini and Temash will be on a 28 nm process node, as compared to 40 nm for Brazos and Hondo.
The real news on Kabini and Temash is in the fine print at the bottom. While Temash will have both dual- and quad-core versions, the quad core version is the A6-1450. It will feature four Jaguar cores at 1 GHz. Temash has a 3D Mark benchmark score more than double that of Hondo, which would put it roughly on par with current Brazos E-series chips.
A Kabini quad core chip will be marketed as the A6-5200. AMD doesn't specify the clock speed, but based on PC Mark benchmark scores, it looks like it will be around 1.7 GHz, as it gets about 1.7 times the score of Temash. Don't take that as a prediction, though, as there could easily be some sort of turbo core that changes results. AMD didn't give graphical benchmark scores on Kabini.
While both Kabini and Temash will have GCN graphics, AMD didn't say how many CUs they'll have. I'm guessing two, with Temash clocking them lower and Kabini higher. But it could just be one, with Temash clocking that one higher, and then Kabini graphics not being that much faster than Temash. For comaparion, a Radeon HD 7770 has 10, a 7870 has 20, and a 7970 has 32--and those all clock them much higher than Kabini will.
Kabini will have a TDP of 9-15 W. I'm guessing that means 9 W for the dual core and 15 W for the quad core, though they could make a low clocked quad core with a TDP of 9 W. According to older rumors, Temash is going to have a TDP of 4.5 W for the dual core and 5.9 W for the quad core.