Cheney lived with a no-pulse artificial heart for 20 months. Obvious jokes aside, it seems the difference is that Cheney's device only assisted the left ventricle, while this was a whole-heart replacement.

Seems like the step from his LVAD to a smooth-pumping artificial heart wasn't nearly as revolutionary as this article makes it sound, however. Both are intended as interim solutions until a donor (flesh) heart can be implanted.