Yes, both OS X and iOS apps. It probably wouldn't be restricted to Mac App Store for OS X apps.
What I'm saying is that it's the same OS in both environments, it's just iOS is optimized for the touchscreen and OS X with non-touch display/keyboard/mouse.
It would be fairly easy for Apple to provide both in the same device if there's a way to use OS X easily since it really isn't comfortable to use on a touchscreen. In this case, a thin detachable keyboard+touchpad might be enough. They certainly have some patents on such a detachable part.
An example would be Surface Pro, Metro = iOS and the "classic" desktop = OS X. Imagine on day one of this device, 1 million iOS apps already ready to go in addition to the OS X apps.
Very interesting. Hypothetically speaking, if Apple implements what you mention, I'm curious if they can pull it off with their own custom ARM-based processor or would they need to go with an Intel processor?