Those are GM speak for different chassis'. An a-body is a chevelle/ elcamino/ lemans, gto, skylark because they all share the same chassis. F-body is the camaro/firebird, the Nova is an X-body. Unibody is the type of chassis where there is no full frame, but a welded in rear subframe and a removeable front frame as are Novas are. Nova's, Camaros, Mustangs, Falcons, and most MOPARS are unibodys but GM seems to be the only manufacture that has the removeable front subframe. All Ford and Mopar front frames are welded on, hence the name "unibody". Chevelles and the like are full frame cars.
A body is Chevelle, Cutlass, Skylark, Lemans
F body is Camaro, Firebird.
Unibody is a car that has no seperate body and frame. The body components are welded together to create one unitized structure. Most modern cars are unibody design. Most trucks, Chevelles, Impalas are full frame type vehicles.
The later Novas are X body, I'm not sure about your 63.
It would be a unibody vehicle since it has no seperate frame.