In Boolean union, the geometry of the overlapping area is eliminated and a single object is created from the two using all of the exposed surface area. Union is generally used to merge objects that are most easily built from component parts that have been modeled separately.
Boolean subtraction is used to sculpt out the overlapping volume from one object or the other.
After the operation, one object is left, minus its overlapping region with the other object. Boolean intersection preserves the overlapping region only, eliminating all the rest of both objects. Boolean operations are very computationally intensive, and often do not work reliably even with the most powerful applications and processors. Booleans are especially unwieldy with complex surfaces, and good modeling often requires careful planning for Boolean operations. If at all possible, Boolean operations should be performed at the earlier, and simpler, stages of modeling.