The two terms have nothing to do with each other. A hybrid is a vehicle which is powered by a gasoline (or sometimes diesel) engine; combined with an electric motor. This type of drive system can be used in a sedan, truck, station wagon, convertible, SUV, motorcycle, or any other type of vehicle. The Toyota Prius is the most common example of a Hybrid. Hybrids typically can run entirely on electric power when driven in city use. That greatly reduces pollution, and reduces fuel cost. The electric motor and the batteries that energize it usually are not powerful enough to drive the vehicle at freeway speeds; so this is where the gas or diesel engine is used to add power to the system.
The term crossover is a new word someone coined to describe a vehicle which has some of the features of a station wagon or van, and some of rhe features of an SUV. Compared to SUVs; crossovers look more like regular cars. They do not sit as high as an SUV, and usually have smaller wheels. But crossovers often come with 4 wheel drive; without requiring the buyer to drive a vehicle with a macho image. And that is probably the heart of their purpose and appeal.
The Saturn VUE would probably fit into the crossover category, because it is available with optional all wheel drive. The Saturn VUE is also available with an optional hybrid drive system. And that is where the confusion probably came from.