Single Mode is where both TV1 and TV2 outputs display the same thing and the receiver functions at one. Yes you would be able to record something on one tuner and watch something on the other.
In Dual mode you can do the same thing as well, but TV1 and TV2 have independent controls and views, so if you want to watch something and record something on the other TV you can do it, you just specify that you want your recording done on the other TV