Wikipedia lists both the model X and Y as "crossover SUVs", though to my sedan-buying eyes the X looks like a standard SUV and the Y doesn't. Not sure what to say. Wikipedia says SUV, my eyes say SUV.
The need for the "crossover" qualifier says it all, IMO. It's a slightly taller station wagon, not something I'm going to take 10 miles down pock-marked forest roads.