The difference primarily seems to derive from how objective moral theory asserts morals as intrinsic properties while subjective moral theory claims morals are descriptive properties. Quite frankly, it's a highly convoluted, complicated, and in my honest opinion, wasteful debate. People have committed atrocities and encroachments upon other's dignity, health, and well being under both sets of philosophical outlooks. It only becomes a meaningful topic of discussion when rather serious conflicts in morality arise between different cultures and/or individuals. Within the areas of overlap, it's just wispy fluff of scant utility.
freedomfromfallacy » I'm weighing my tears to see if the happy ones weigh the same as the sad ones.