SUV = Sports Utility Vehicle.,
Crossover to me means a part time AWD that only works when the drive wheels, usually the front ones lose traction and the other wheels get power to them to help get out of slippery conditions.
Subaru are full time AWD and there may be others as well.
AWD should not be confused with proper 4WD?s that are made for rough off road work.
Companies are all making SUV's of various sizes as they are 1 of the best selling types today. Having an SUV for a DD or taking the kids to school is a bit like people that get around in gym gear that don't actually go to a gym so they are worn as a fashion.
Hope that makes sense ?