With casting, you are not modifying the object. The result of the cast is still the exact same object, just with a difference type of reference pointing to it:
With conversion, you are taking the source object and (in most cases) returning a new object based on the old one:
Bob, can you please finish that second link? It doesn't point anywhere valid right now, and if I just go to the forum I have to do a search there. I might as well link to our own search.