What you skin is based off the mob and the mob's level. You can get medium level off level 15s, but it's a really low chance; once you get closer to 20, it starts to become more common, and by 25 you'll hardly ever get light leather, and probably start hitting heavy. Hides work the same way, so far as I can tell, but you have a much smaller chance of getting a hide than of getting leather.
Skinning skill is just for what level monster you can skin, and how likely you are to not fail skinning it.