The 3rd tool is the Intersect tool and it results in a shape that is the intersection of the selected shapes. Any part of the shapes that aren’t overlapping are removed. (The tools doesn’t work if you have text in the shapes.)
Here’s an example of a slide that I created using Intersect:
I created the gold-colored shape in the middle using Intersect.
In order to accomplish this, because the shapes have text, I created duplicates of each circle without text. I placed them exactly on top of the original circles.
By the way, I originally created the circles using SmartArt and then ungrouped it twice so I had individual objects.
To create the intersect shapes, just select the shapes and click the Intersect button. When I did that, the duplicate circles were deleted and I ended up with just the overlap in the center. I recolored that shape to make it stand out. Then I added an Appear animation to the intersect shape.