People are generally referring to them as "Shaped" skis and "Carving" is the technique that is being used to ski them.
One of the biggest differences I see between straight ski users and shaped ski users is the distance between the feet. Old straight plankers are keeping their feet so tight together they can pinch a quarter between their boots. While new ski "carvers" are keeping them about 6-12" apart and letting the parabolic shape do what it was designed to do.
I'd recommend a demo coupled with a lesson to focus on carving technique.