Crossovers are unibody based while traditional SUV's are full-framed. Unibody offers lower weight, better space utilization and generally better gas mileage. However, they are not quite as rugged as a full-framed SUV and generally don't have the off-road capability or towing capacity.
It's just marketing terms. Other manufacturers have tried other monikers and acronyms in the past, such as "Sport Activity Vehicle", in an attempt to differentiate their product from the competition. Perhaps "Crossover" will stick better than another alphabet soup... SUV is pretty ingrained in the common vernacular.
BTW, unless I'm crazy, there are other "SUV's" on the road that aren't build body-on-frame already, or at the very least don't use ladder frames.