"Whose apple is this?"
Translation:Bu elma kimin?
the difference is a bit subtle to explain but here it goes:
"kimin elmasi bu" is emphasizing the question about the owner of the apple in literal translation Who is it that owns this apple? Or alternatively To whom this apple belongs to?, Who is the apple's owner?
In the "Bu elma kimin?" it is more like emphasizing on the apple, querying about the properties of the apple as in "This apple belongs to who?". So in this case it implies a tiny bit of continuation. If I get an answer to this question I will ask more about it.