The Union tool is a Booleans operation. It takes two objects (that are overlapping) and deletes any faces that aren't visible, or required to form the overall shape.

The combine tool take 2 or more objects and, well, combines them, but doesn't delete any geometry. And so these objects can be separated at a later point if the need be.

The reason the Union tool might not be working is maybe you don't have the objects overlapping? If not, maya's Booleans operations are known to have issues.