Hi Robert,
> So what exactly is going on?
Most likely you're getting different results at different times due to the specific places where you are placing your revolve axis - the points where you place the revolve axis will also determine where the pole and the "seam edge" of the sphere are located at, and booleans can be more sensitive when seam edges overlap over other edges in awkward ways.
Try to be more precise with the placement of the revolve axis putting the endpoints right on the quadrant points of the circle, that may help. Or also if you use Draw solid > Sphere rather than revolve for this case, that will orient the sphere differently from how you are doing it, with the sphere's "pole" point going vertically as well rather than overlapping right along the cylinder's bottom edge.
> Unioning two objects should "always" produce the same results, right?
Well, in theory yes but in practice part of the boolean process involves intersecting edges that collide into one another and so the specific arrangement of edges to other edges can have an impact and certain edge configurations especially if things are overlapping but not quite synchronized to each other very exactly can be more difficult for the merging process to handle.
- Michael
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