Psychobabble.............
Nope. Real difference. Probably the cognitive basis for the predominance of males in engineering, for one thing. Simple every day experience for another: try giving directions to a woman by saying go east three miles and turn south on Route 21. They usually will stare at you blankly. You're better off telling them to go straight ahead to the corner with the BP station and then turn right at the light.
No, a very real effect. The brain needs testosterone to process spatial information. Women do have some testosterone, but not nearly as much as a man does. (A thought that, no doubt, horrifies the average, Oprah-cized, White, liberal male!) Men are thus more skilled at seeing objects in three dimensions. Women usually cannot imagine an object in three dimensions and see it rotating in space.