In C.S. Lewis' The Magician's Nephew, Aslan modifies a normal horse to make him a talking horse and then later gives him wings and makes him a flying, talking horse. What if he transformed him further so that he looked and acted just like a human? Would he be a horse still? Would he be human?
I have wonder this before, but regarding the middle earth beings of JRR Tolkein. For example, what is it that distinguishes dwarves from hobbits? It seems to be accidental qualities or perhaps some causal history or something.
They do have different accidental qualities. Dwarves are taller and stockier. They have very different temperaments and lifestyles. But they also have a very different causal history. Hobbits are related to humans. The appendices say that their genealogical connection is lost, but they're closest to humans. Dwarves have a completely different origin story and were created by the Vala Aulë, whereas elves and humans were created directly by Iluvatar (God).