Having been a suspension engineer and vehicle dynamicist, I can shed a little light on this. The chassis is the overall term for the undercar bits and what they attach to. The suspension parts are the ones that move. The frame or unit body provides the connection between the front and rear suspensions and the mounting for the engine. All these things combine to provide the car’s handling.
Engineers want the structure that the suspension attaches to as rigid as possible so that the suspension can isolate bumps, provide directional control and carry loads. The go-kart is a good example of what happens when a stiff suspension (basically, none) is attached to a flexible frame, the frame BECOMES the suspension and can’t be controlled as well with shocks (none) springs (the frame itself) and stabilizer bars (again the frame). You can never get as much structure as you want because it is heavy, expensive and the car needs to carry people and stuff. The compromise we make is different from a luxury sedan to a sports car.
The magazine writers are driving the car and evaluating how smooth it rides, how well it responds to steering, braking and acceleration (the handling) as they drive the car normally to tire slidin’ fun. They evaluate how well it changes direction, comes back to and stays straight, the limits of traction, cornering and stopping all with the idea of what the buyer expects. Car companies have experts (much better ones!) who do this day in and out.